Forecasting Models for the German Office Market

Forecasting Models for the German Office Market
DISSERTATION
of the University of St. Gallen
Graduate School of Business, Administration,
Economics, Law and Social Sciences (HSG)
to obtain the title of
Doctor of Economics
Submitted by
Alexander Bönner
from
Germany
Approved on the application of
Prof. Dr. Pascal Gantenbein
and
Prof. Dr. Klaus Spremann
Dissertation no. 3561
GABLER VERLAG WIESBADEN, 2009
The University of St.Gallen, Graduate School of Business
Administration, Economics, Law, and Social Science (HSG) hereby
consents to the printing of the present dissertation, without hereby
expressing any opinion on the views herein expressed.
St. Gallen, November 21, 2008
The President
Prof. Ernst Mohr, PhD
Die Arbeit erscheint unter dem Titel
Alexander Bönner: Forecasting Models for the German Office Market
in der Reihe GABLER EDITION WISSENSCHAFT
mit der ISBN: 978-3-8349-1525-2 im Gabler Verlag, Wiesbaden, 2009
Alexander Bönner
Forecasting Models for the German Office Market
GABLER EDITION WISSENSCHAFT
Alexander Bönner
Forecasting Models for
the German Office Market
GABLER EDITION WISSENSCHAFT
Bibliographic information published by the Deutsche Nationalbibliothek
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detailed bibliographic data are available in the Internet at http://dnb.d-nb.de.
Dissertation Universität St. Gallen, 2009
1st Edition 2009
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V
Acknowledgements
First and foremost, I would like to express my deepest gratitude to my thesis
supervisor and academic mentor, Prof. Dr. Pascal Gantenbein. His guidance and ideas
in numerous discussions led me to many new insights into my topic. I also want to
thank him for his patience when I was choosing my topic and setting the focus of my
work. Moreover, his flexibility after his appointment to the professorship of Financial
Management at the University of Basle was not a matter of course. Thus, he
contributed immensely to the success of my dissertation
Furthermore, I would like to thank Prof. Dr. Dr. h.c. Klaus Spremann for cosupervising my dissertation and providing highly valuable input. Working at his chair
at the Swiss Institute of Banking and Finance at the University of St. Gallen was a
great honor. Embedded in an enjoyable and open-minded atmosphere, I was able to
deepen my finance and personal skills through several projects, teaching opportunities,
research work, and lecture support.
On this note I also want to thank all my colleagues and friends at the Swiss
Institute of Banking and Finance, in the “WG” or back home in Germany. While I
cannot recognize each of them individually, I would like to mention Roman Frick and
Patrick Scheurle, who gave me invaluable impulses throughout the long work on my
dissertation and Stefan Morkötter, whose ideas in various discussions represented
important steps on the path to my final dissertation topic.
I also want to acknowledge Feri EuroRating Services AG, who kindly provided
most of the data employed. In particular, I would like to thank Manfred Binsfeld for
his informal support.
Last but not least, words of deep gratitude go to my family, my parents, Dr. jur.
Max Bönner and Monika Bönner, and my brothers, Dr. med. Florian Bönner and Dr.
jur. Maximilian Bönner. I dedicate this dissertation to them for their motivating words
in the valleys that I had to pass through on my way to the completion of this work,
their ever-present care, and their support throughout the years.
St. Gallen, January 2009
Alexander Bönner
VII
Contents
CONTENTS .............................................................................................................. VII
SUMMARY .................................................................................................................XI
SUMMARY (GERMAN) ......................................................................................... XII
LIST OF TABLES ...................................................................................................XIII
LIST OF GRAPHS ................................................................................................... XV
LIST OF ABBREVIATIONS ................................................................................. XIX
1.
2.
3.
INTRODUCTION ................................................................................................. 1
1.1.
General Motivation ....................................................................................................................... 1
1.2.
Research Questions ....................................................................................................................... 2
1.3.
Outline of the dissertation ............................................................................................................ 3
LITERATURE REVIEW..................................................................................... 5
2.1.
Multivariate regression models .................................................................................................... 5
2.2.
Univariate models.......................................................................................................................... 8
2.3.
VAR and VEC models ................................................................................................................ 10
THEORETICAL FOUNDATIONS................................................................... 12
3.1.
General real estate market characteristics................................................................................ 12
3.1.1.
Definiton of the terms real estate and real estate market ..................................................... 12
3.1.2.
The four quadrant model according to DiPasquale and Wheaton........................................ 13
3.1.3.
Real estate market characteristics ........................................................................................ 17
3.2.
Specifics of time series and panel data ...................................................................................... 18
3.2.1.
Definition of time series data............................................................................................... 19
3.2.2.
Definition of panel data ....................................................................................................... 19
3.2.3.
Stationarity........................................................................................................................... 20
3.2.4.
Cointegration ....................................................................................................................... 21
VIII
3.3.
Theoretical fundamentals of common forecasting models....................................................... 21
3.3.1.
Multivariate regression model ............................................................................................. 22
3.3.2.
ARIMA model..................................................................................................................... 24
3.3.3.
GARCH model .................................................................................................................... 26
3.3.4.
VAR and VEC models......................................................................................................... 28
3.3.5.
Evaluation of the examined forecasting models .................................................................. 30
3.4.
Forecasting techniques and forecasting performance measures............................................. 32
3.4.1.
Forecasting techniques......................................................................................................... 33
3.4.2.
Forecasting performance measures...................................................................................... 34
4.
DESIGN OF THE EMPIRICAL STUDY......................................................... 36
4.1.
Research hypotheses ................................................................................................................... 36
4.2.
Research methodology ................................................................................................................ 38
4.3.
Data .............................................................................................................................................. 41
4.3.1.
Rent series............................................................................................................................ 42
4.3.2.
Total Yield series................................................................................................................. 42
4.3.3.
Potentially explanatory variables......................................................................................... 43
5.
EMPIRICAL RESULTS: RENT FORECASTING......................................... 45
5.1.
Univariate models........................................................................................................................ 45
5.1.1.
Rent data analysis ................................................................................................................ 45
5.1.2.
ARIMA models: Construction, estimation, and forecasting ................................................ 53
5.1.3.
GARCH models: Construction, estimation, and forecasting ............................................... 66
5.1.4.
Conclusion ........................................................................................................................... 70
5.2.
Multivariate regression models .................................................................................................. 71
5.2.1.
Explanatory variables analysis............................................................................................. 71
5.2.2.
Model construction and estimation...................................................................................... 73
5.2.3.
Discussion of the city rent series forecasts .......................................................................... 75
5.2.4.
Conclusion ........................................................................................................................... 85
5.3.
Comparison of univariate and multivariate models................................................................. 86
5.3.1.
Comparison and interpretations ........................................................................................... 86
5.3.2.
Conclusion ........................................................................................................................... 95
5.4.
Long-run forecasting models...................................................................................................... 96
5.4.1.
Determination and interpretation ......................................................................................... 97
5.4.2.
Conclusion ......................................................................................................................... 103
5.5.
Chapter Conclusion................................................................................................................... 104
IX
6.
EMPIRICAL RESULTS: TOTAL YIELD FORECASTING ...................... 108
6.1.
Total yield series analysis ......................................................................................................... 108
6.1.1.
Total yield data description................................................................................................ 108
6.1.2.
Interpretations and conclusions ......................................................................................... 115
6.2.
Multivariate models .................................................................................................................. 117
6.2.1.
Explanatory variables analysis........................................................................................... 117
6.2.2.
Model construction and estimation.................................................................................... 119
6.2.3.
Discussion of the city total yield series forecasts .............................................................. 120
6.2.4.
Conclusion ......................................................................................................................... 130
6.3.
Long-run forecasting models.................................................................................................... 131
6.3.1.
Determination and interpretation ....................................................................................... 131
6.3.2.
Conclusion ......................................................................................................................... 138
6.4.
7.
Chapter Conclusion................................................................................................................... 140
CONCLUSION .................................................................................................. 142
7.1.
Summary of findings................................................................................................................. 142
7.2.
Implications for practice........................................................................................................... 144
7.3.
Research Outlook ...................................................................................................................... 145
APPENDIX................................................................................................................ 147
REFERENCES.......................................................................................................... 168
XI
Summary
This work is motivated by the research gap evident in the area of forecasting models
for the German office market. Since rent, price or yield forecasting research is mainly
done by commercially oriented organizations, this work delivers an examination from
a scientific point of view. Thus the focus is set on an empirical investigation of several
rent and total yield forecasting models for nine major German cities. Their
applicability and performance are analyzed and city as well as forecasting horizonspecific patterns are determined and interpreted.
After the literature review, mainly covering Anglo-Saxon research, I derive the
theoretical foundations which are important in executing the empirical part of the
work. Therefore, I discuss theoretically general real estate market characteristics, the
specifics of time series and panel data, common forecasting models, and forecasting
techniques as well as performance measures.
The major findings of the first part of the empirical work, which contains the rent
series investigation, is that ARIMA, GARCH and multivariate regression models are
generally able to forecast rent series in the German office market. Furthermore, I
observed that GARCH models are able to outperform single ARIMA models for
forecasting horizons of three to five years, when increased volatility appears within the
respective city rent series. Moreover, univariate models outperform multivariate
regression models in the short run. On the other hand, multivariate regression models
outperform the univariate models in the longer run. However, I found cities where one
model permanently dominates. Furthermore, parsimoniously constructed multivariate
regression models lead to considerably better forecasting performances than more
complex multivariate ones. For the long run I also show that the rent level is mainly
determined by its economic fundamentals. Nevertheless, precise forecasts require
starting values at economically reasonable rent levels.
The major finding of the second part of the empirical work, which contains the
total yield series investigation, is the general ability of multivariate regression models
to forecast total yield series in the German office market. Again, parsimoniously
constructed models outperform more complex models for the short run and for the
long run. For the long run, I additionally demonstrate that the total yield is mainly
determined by its economic fundamentals. The rent analysis prerequisite of starting
values at economically reasonable levels cannot be neglected but can be relativized to
some extent.
XII
Summary (German)
Dieses Buch ist motiviert durch die Forschungslücke im Bereich der Prognosemodelle
für den deutschen Büroimmobilienmarkt. Miet-, Preis- oder Yieldprognosemodelle
werden hauptsächlich von kommerziell arbeitenden Instituten erstellt. Diese Arbeit ist
aus akademisch wissenschaftlicher Perspektive geschrieben und setzt den Fokus auf
empirische Untersuchungen verschiedener Miet- und Total Yield Prognosemodelle für
neun bedeutende deutsche Städte. Die Analyse zielt auf deren Anwendbarkeit und
Performance für die verschiedenen Städte und für verschiedene Prognosehorizonte.
Nach Darstellung der massgeblichen, hauptsächlich angelsächsischen Literatur
zu Immobilienprognosemodellen werden die theoretischen Grundlagen für den
empirischen Teil der Arbeit gelegt. Neben allgemeinen Immobilienmarktcharakteristika werden auch die Besonderheiten von Zeitreihen- und Paneldaten, grundlegende
Prognosemodelle wie auch Prognosetechniken und Performancemasse dargestellt.
Die Haupterkenntnisse des ersten Teils der Empirie, der Mieten untersucht, sind,
dass ARIMA, GARCH und multivariate Regressionsmodelle grundsätzlich für
Mietprognosen im deutschen Büroimmobilienmarkt geeignet sind. Es wird weiterhin
beobachtet, dass GARCH Modelle eine höhere Prognosegüte als ARIMA Modelle im
drei bis fünf Jahres Prognosehorizont erzielen, wenn in den untersuchten Städten
erhöhte Volatilität feststellbar ist. Ebenso wird festgestellt, dass univariate Modelle die
multivariaten Regressionsmodelle bzgl. der Prognosegüte in der kurzen Frist
übertreffen. Das Gegenteil ist der Fall in der langen Frist. Abweichend von diesem
Grundmuster gibt es allerdings Städte in denen eine Modellart permanent dominant ist.
Es stellt sich auch heraus, dass Regressionsmodelle mit wenigen Faktoren höhere
Prognosegüte liefern als solche mit komplexen Strukturen. Weiterhin lässt sich zeigen,
dass das Mietniveau in der langen Frist hauptsächlich durch ökonomische
Zusammenhänge bestimmt ist, präzise Prognosen allerdings Startwerte auf
ökonomisch nachvollziehbarem Niveau benötigen.
Die Haupterkenntnisse des zweiten Teils der Empirie, der Total Yields
untersucht, sind, dass multivariate Regressionsmodelle grundsätzlich für Total Yield
Prognosen im deutschen Büroimmobilienmarkt geeignet sind. Ebenso stellt sich
heraus, dass Regressionsmodelle mit wenigen Faktoren höhere Prognosegüte liefern
als solche mit komplexen Strukturen. Weiterhin lässt sich zeigen, dass das Total Yield
Niveau in der langen Frist hauptsächlich durch ökonomische Zusammenhänge
bestimmt ist. Im Gegensatz zur Mietuntersuchung sind Startwerte auf ökonomisch
nachvollziehbarem Niveau für präzise Prognosen weniger wichtig.
XIII
List of Tables
Table 1: Model overview ...................................................................................................................... 32
Table 2: ARIMA Rent Model Forecast Outcomes – Cologne .............................................................. 54
Table 3: ARIMA Rent Model Forecast Outcomes – Dusseldorf .......................................................... 56
Table 4: ARIMA Rent Model Forecast Outcomes – Essen................................................................... 57
Table 5: ARIMA Rent Model Forecast Outcomes – Frankfurt ............................................................. 59
Table 6: ARIMA Rent Model Forecast Outcomes – Hamburg ............................................................. 60
Table 7: ARIMA Rent Model Forecast Outcomes – Munich ............................................................... 62
Table 8: ARIMA Rent Model Forecast Outcomes – Nuremberg .......................................................... 63
Table 9: ARIMA Rent Model Forecast Outcomes – Stuttgart .............................................................. 65
Table 10: GARCH Rent Model Forecast Outcomes – Frankfurt .......................................................... 66
Table 11: Comparison: Univariate Rent Models – Frankfurt ................................................................ 67
Table 12: GARCH Rent Model Forecast Outcomes – Munich ............................................................. 68
Table 13: Comparison: Univariate Rent Models – Munich .................................................................. 69
Table 14: Correlation analysis: Rent vs. potential explanatory variables ............................................. 72
Table 15: Multivariate Regression Rent Model Forecast Outcomes – Cologne ................................... 75
Table 16: Multivariate Regression Rent Model Forecast Outcomes – Dusseldorf ............................... 76
Table 17: Multivariate Regression Rent Model Forecast Outcomes – Essen ....................................... 77
Table 18: Multivariate Regression Rent Model Forecast Outcomes – Frankfurt .................................. 78
Table 19: Multivariate Regression Rent Model Forecast Outcomes – Hamburg .................................. 79
Table 20: Multivariate Regression Rent Model Forecast Outcomes – Leipzig..................................... 80
Table 21: Multivariate Regression Rent Model Forecast Outcomes – Munich .................................... 82
Table 22: Multivariate Regression Rent Model Forecast Outcomes – Nuremberg............................... 83
Table 23: Multivariate Regression Rent Model Forecast Outcomes – Stuttgart ................................... 84
Table 24: Rent Forecast Outcomes -Cologne- Comparison Univariate vs. Multivariate Models ......... 86
Table 25: Rent Performance Measure Comparison – Cologne ............................................................. 87
Table 26: Rent Forecast Outcomes -Dusseldorf- Comparison Univariate vs. Multivariate Models ..... 87
Table 27: Rent Performance Measure Comparison – Dusseldorf ......................................................... 88
Table 28: Rent Forecast Outcomes -Essen- Comparison Univariate vs. Multivariate Models ............. 89
Table 29: Rent Performance Measure Comparison – Essen ................................................................. 89
Table 30: Rent Forecast Outcomes -Frankfurt- Comparison Univariate vs. Multivariate Models ....... 90
XIV
Table 31: Rent Performance Measure Comparison – Frankfurt............................................................ 90
Table 32: Rent Forecast Outcomes -Hamburg- Comparison Univariate vs. Multivariate Models ....... 91
Table 33: Rent Performance Measure Comparison – Hamburg............................................................ 91
Table 34: Rent Forecast Outcomes -Munich- Comparison Univariate vs. Multivariate Models .......... 92
Table 35: Rent Performance Measure Comparison – Munich .............................................................. 92
Table 36: Rent Forecast Outcomes -Nuremberg- Comparison Univariate vs. Multivariate Models .... 93
Table 37: Rent Performance Measure Comparison – Nuremberg ........................................................ 93
Table 38: Rent Forecast Outcomes -Stuttgart- Comparison Univariate vs. Multivariate Models ......... 94
Table 39: Rent Performance Measure Comparison – Stuttgart ............................................................. 94
Table 40: Correlation analysis: Total Yield vs. potential explanatory variables ................................. 117
Table 41: Multivariate Regression Total Yield Model Forecast Outcomes – Cologne ...................... 121
Table 42: Multivariate Regression Total Yield Model Forecast Outcomes – Dusseldorf .................. 122
Table 43: Multivariate Regression Total Yield Model Forecast Outcomes – Essen ........................... 123
Table 44: Multivariate Regression Total Yield Model Forecast Outcomes – Frankfurt ..................... 124
Table 45: Multivariate Regression Total Yield Model Forecast Outcomes – Hamburg ..................... 125
Table 46: Multivariate Regression Total Yield Model Forecast Outcomes – Leipzig ........................ 126
Table 47: Multivariate Regression Total Yield Model Forecast Outcomes – Munich........................ 127
Table 48: Multivariate Regression Total Yield Model Forecast Outcomes – Nuremberg .................. 128
Table 49: Multivariate Regression Total Yield Model Forecast Outcomes – Stuttgart ...................... 129
XV
List of Graphs
Graph 1: Four-quadrant model .............................................................................................................. 15
Graph 2: Cologne Rent Series ............................................................................................................... 46
Graph 3: Dusseldorf Rent Series .......................................................................................................... 46
Graph 4: Essen Rent Series ................................................................................................................... 47
Graph 5: Frankfurt Rent Series ............................................................................................................. 48
Graph 6: Hamburg Rent Series ............................................................................................................. 49
Graph 7: Leipzig Rent Series ................................................................................................................ 49
Graph 8: Munich Rent Series ................................................................................................................ 50
Graph 9: Nuremberg Rent Series .......................................................................................................... 51
Graph 10: Stuttgart Rent Series ............................................................................................................. 52
Graph 11: ARIMA Rent Model Forecast Outcomes – Cologne ........................................................... 55
Graph 12: ARIMA Rent Model Forecast Outcomes – Dusseldorf ....................................................... 56
Graph 13: ARIMA Rent Model Forecast Outcomes – Essen ................................................................ 58
Graph 14: ARIMA Rent Model Forecast Outcomes – Frankfurt .......................................................... 60
Graph 15: ARIMA Rent Model Forecast Outcomes – Hamburg .......................................................... 61
Graph 16: ARIMA Rent Model Forecast Outcomes – Munich............................................................. 62
Graph 17: ARIMA Rent Model Forecast Outcomes – Nuremberg ....................................................... 64
Graph 18: ARIMA Rent Model Forecast Outcomes – Stuttgart ........................................................... 65
Graph 19: GARCH Rent Model Forecast Outcomes – Frankfurt ......................................................... 67
Graph 20: GARCH Rent Model Forecast Outcomes – Munich ............................................................ 69
Graph 21: Multivariate Regression Rent Model Forecast Outcomes – Cologne .................................. 75
Graph 22: Multivariate Regression Rent Model Forecast Outcomes – Dusseldorf .............................. 77
Graph 23: Multivariate Regression Rent Model Forecast Outcomes – Essen....................................... 78
Graph 24: Multivariate Regression Rent Model Forecast Outcomes – Frankfurt ................................. 79
Graph 25: Multivariate Regression Rent Model Forecast Outcomes – Hamburg ................................. 80
Graph 26: Multivariate Regression Rent Model Forecast Outcomes – Leipzig .................................... 81
Graph 27: Multivariate Regression Rent Model Forecast Outcomes – Munich ................................... 82
Graph 28: Multivariate Regression Rent Model Forecast Outcomes – Nuremberg .............................. 83
Graph 29: Multivariate Regression Rent Model Forecast Outcomes – Stuttgart .................................. 84
Graph 30: Long-Run Rent Model Forecast Outcomes – Cologne ........................................................ 97
XVI
Graph 31: Long-Run Rent Model Forecast Outcomes – Dusseldorf .................................................... 98
Graph 32: Long-Run Rent Model Forecast Outcomes – Essen............................................................. 98
Graph 33: Long-Run Rent Model Forecast Outcomes – Frankfurt ....................................................... 99
Graph 34: Long-Run Rent Model Forecast Outcomes – Hamburg ..................................................... 100
Graph 35: Long-Run Rent Model Forecast Outcomes – Leipzig ........................................................ 100
Graph 36: Long-Run Rent Model Forecast Outcomes – Munich ....................................................... 101
Graph 37: Long-Run Rent Model Forecast Outcomes – Nuremberg .................................................. 102
Graph 38: Long-Run Rent Model Forecast Outcomes – Stuttgart ...................................................... 102
Graph 39: Cologne Total Yield Series ................................................................................................ 109
Graph 40: Dusseldorf Total Yield Series ............................................................................................ 110
Graph 41: Essen Total Yield Series..................................................................................................... 110
Graph 42: Frankfurt Total Yield Series ............................................................................................... 111
Graph 43: Hamburg Total Yield Series ............................................................................................... 112
Graph 44: Leipzig Total Yield Series.................................................................................................. 112
Graph 45: Munich Total Yield Series ................................................................................................. 113
Graph 46: Nuremberg Total Yield Series ............................................................................................ 114
Graph 47: Stuttgart Total Yield Series ................................................................................................ 114
Graph 48: Multivariate Regression Total Yield Model Forecast Outcomes – Cologne...................... 121
Graph 49: Multivariate Regression Total Yield Model Forecast Outcomes – Dusseldorf.................. 122
Graph 50: Multivariate Regression Total Yield Model Forecast Outcomes – Essen .......................... 123
Graph 51: Multivariate Regression Total Yield Model Forecast Outcomes – Frankfurt .................... 124
Graph 52: Multivariate Regression Total Yield Model Forecast Outcomes – Hamburg .................... 125
Graph 53: Multivariate Regression Total Yield Model Forecast Outcomes – Leipzig ....................... 126
Graph 54: Multivariate Regression Total Yield Model Forecast Outcomes – Munich ....................... 128
Graph 55: Multivariate Regression Total Yield Model Forecast Outcomes – Nuremberg ................. 129
Graph 56: Multivariate Regression Total Yield Model Forecast Outcomes – Stuttgart ..................... 130
Graph 57: Long-Run Total Yield Model Forecast Outcomes – Cologne............................................ 132
Graph 58: Long-Run Total Yield Model Forecast Outcomes – Dusseldorf........................................ 132
Graph 59: Long-Run Total Yield Model Forecast Outcomes – Essen ................................................ 133
Graph 60: Long-Run Total Yield Model Forecast Outcomes – Frankfurt .......................................... 134
Graph 61: Long-Run Total Yield Model Forecast Outcomes – Hamburg .......................................... 135
Graph 62: Long-Run Total Yield Model Forecast Outcomes – Leipzig ............................................. 135
XVII
Graph 63: Long-Run Total Yield Model Forecast Outcomes – Munich ............................................. 136
Graph 64: Long-Run Total Yield Model Forecast Outcomes – Nuremberg ....................................... 137
Graph 65: Long-Run Total Yield Model Forecast Outcomes – Stuttgart ........................................... 137
XIX
List of Abbreviations
AR(p)
Autoregressive Process
ARCH
Autoregressive Conditional Heteroskedasticity
ARCH-M
Autoregressive Conditional Heteroskedasticity -in-mean
ARIMA(p,i,q)
Autoregressive Integrated Moving Average Process
ARIMAX
Autoregressive, Integrated,
explanatory variable
ARMA
Autoregressive Moving Average Process
BGB
Bürgerliches Gesetzbuch (German Civil Code)
C
Construction level
CCosts
Replacement costs
D
Demand for space
e.g.
For example
EGARCH
Exponential Generalized
Heteroskedasticity
et al.
Et alii (and others)
etc.
Et cetera (and so on)
e.V.
Eingetragener Verein (registered association)
f. / ff.
And the following page / -s
f(.)
Function of (.)
GAR
Generalized Autoregressive Process
GARCH
Generalized Autoregressive Conditional
Heteroskedasticity
GDP
Gross Domestic Product
i
Capitalization rate
LM
Lagrange multiplier
MA(q)
Moving Average Process
Moving
Average
Autoregressive
plus
Conditional
XX
MAPE
Mean Absolute Percentage Error
MSA
Metropolitan Statistical Area
OLS
Ordinary Least Squares
P
Price per unit
p.
Page / -s
§
Article (law)
R
Rent per unit
R²
R-squared
RMSE
Root Mean Square Error
S
Stock of space
SBC
Schwartz Bayesian Criterion
TARCH
Threshold Autoregressive Conditional
Heteroskedasticity
UK
United Kingdom
US/ USA
United States of America
VAR
Vector Autoregressive
VEC
Vector Error Correction
ZGB
Zivilgesetzbuch (Swiss Civil Code)
1
1.
Introduction
1.1. General Motivation
In every market with free floating prices, all market participants are interested in an
answer to the question of the future developments of those prices. Thus, having an idea
about its future rent and total yield pattern is very advantageous for all participants,
especially investors in the office real estate markets.
As one important source to evaluate an investment opportunity within a portfolio
is the future income stream emanating from the investment, this work focuses on an
examination of rent and total yield forecasts.1 Especially for long-term investors in real
estate, of whom many have an investment horizon of at least a decade, the future real
estate income stream is mainly presented by the future rent. On the other hand, for
short-term investors who are planning to resell their investment in the foreseeable
future, the total yield forecast becomes particularly interesting. Since this measure
comprises the sum of rental and price yields, it is very sensitive to real estate price
appreciations and depreciations.
Since in their groundbreaking paper Case and Shiller (1989) demonstrated that
the US housing market is not informationally efficient and thus does not follow a
random walk, the execution of forecasts is proven to be possible and reasonable. Their
finding is explained by the heterogeneity, illiquidity, and high transaction costs that
underlie real estate markets. As heterogeneity can even be noticed within one country
when considering different cities, brokers or consultants who are only active within a
certain city are not the only parties for whom taking a closer look at specific rent and
total yield developments of single cities is especially interesting. Moreover, knowing
rent and total yield level forecasts or predicted peaks and troughs in the future
development of individual cities is also important for nationally and internationally
operating investors or portfolio managers.
Thus, this work firstly gives a general overview of seminal quantitative scientific
work on property market modeling and forecasting, presenting a range of the most
prominent econometric models currently available. These publications are dominated
by US- and UK-based researchers. Their empirical work mainly focuses on rent as
well as on vacancy rate, price, and yield forecasting.
1
A good overview of the important characteristics and details of portfolio theory is provided by
Spremann (2006).
2
For the German market, real estate rent, price, or yield forecasting research is
mainly done by commercially oriented organizations. Published models as well as
general quantitative work by academic scientists can scarcely be found. Hence, this
work tries to fill this gap for the German office market by examining nine major
German cities with respect to rent and total yield forecasting models. Therefore, in the
split empirical part of this work I apply several prominent econometric models to these
nine markets where possible. I compare the models’ performances and interpret the
patterns found for each of the cities' forecasting results. The first part presents the
results for the rent series; the second part provides evaluations for the total yield series.
1.2. Research Questions
The main objective of this work is to examine the appropriateness and performance of
diverse forecasting models for rent and total yield predictions in the German office
market. Additionally, city specifics and differences concerning the chosen time
horizons are analyzed and interpreted. Presenting results for this research objective
demands further refinement and structuring. Therefore, I formulate four major research
questions, most of which are accompanied by several more detailed sub-questions. The
first question addresses a general investigation of forecasting models currently
available for the real estate market. This question is examined in the literature review.
Questions 2 to 4 are formulated to lead to research hypotheses analyzed in the
empirical study. Question 2 is concerned with an investigation of appropriate rent and
total yield forecasting models for the German office market. Question 3 focuses on the
best performing forecasting models. Finally, question 4 addresses analyses of long-run
forecasting models.
x Research Question 1: Which forecasting models for real estate rents, prices or
total yields are currently applied and discussed in the literature?
x Research Question 2: Which forecasting models are appropriate to forecast rent
series in the German office markets? Are there differences according to the total
yield series?
x Research Question 2.1: Which influence have lagged values of the
respective series?
x Research Question 2.2: Does increased volatility play a role?
3
x Research Question 2.3: Which economic variables and real estate market
indicators have influence on the series?
x Research Question 2.4: Which variables are sufficient to explain the
respective series development?
x Research Question 3: Which forecasting model performs best for the respective
series?
x Research Question 3.1: Are there differences regarding cities?
x Research Question 3.2: Are there differences regarding time horizon?
x Research Question 3.3: How can the detected patterns be interpreted?
x Research Question 4: Which forecasting model is suitable for precise long-run
forecasts?
x Research Question 4.1: Do economic fundamentals play a role?
x Research Question 4.2: Which role play speculative factors?
x Research Question 4.3: How is the "optimal" city-specific forecast starting
value defined?
1.3. Outline of the dissertation
This work is structured as follows. After the introduction, representing the motivation
and the research questions, chapter 2 discusses seminal work on real estate market
modeling focusing on rent, price, yield, or vacancy rate equations. Furthermore, the
important empirical publications concerning model estimations and forecasting are
introduced. In Chapter 3 I discuss theoretically general real estate market
characteristics, time series and panel data specifics, common forecasting models, and
applicable performance measures. Chapter 4 presents the design of the empirical
study. Therefore, research hypotheses and research methodology are stated and the
applied data is defined. Chapter 5 shows the empirical results of the investigation of
the rent series. It starts with a data analysis of the rent series, which is followed by the
construction and estimation of different city-specific univariate models. Subsequently,
these models are used to forecast the rent level. Interpretations conclude this part. The
second part of chapter 5 firstly demonstrates an examination of variables that are
4
chosen to explain the rent development in a multivariate model. After a correlation
analysis, the model is constructed and its coefficients are estimated. Rent forecasts are
conducted and interpreted. In the third part of chapter 5, the outcomes of the univariate
and the multivariate models' forecasts are compared. City- and time-specific patterns
are detected and interpreted. Finally, in the fourth part of chapter 5, models for longrun forecasts are constructed and estimated, and their forecasts are then discussed.
Chapter 6 demonstrates the empirical work on total yield models. It starts with a data
analysis of the total yield series. The next subchapter offers a correlation analysis of
the series with possibly influential indicators. This is followed by the construction and
estimation of a multivariate model, after which total yield forecasts are conducted and
interpreted. The last subchapter shows the construction and estimation of total yield
long-run models. It closes with forecasts and their discussion. Chapter 7 concludes the
dissertation.
5
2.
Literature Review
Groundbreaking work on real estate market forecasting models and their application
was mainly accomplished by the Anglo-Saxon research community. Therefore, the
upcoming chapter focuses on different approaches found in the most prominent
literature. The chapter starts with a more or less chronological overview of the
development and the progress of multivariate regression models in subchapter 2.1.
Subchapter 2.2 provides an outline of the most important findings regarding univariate
model forecasting in the real estate sector. This chapter closes with a summary of the
major publications in the area of Vector Autoregressive (VAR) and Vector Error
Correction (VEC) modeling in the real estate markets.
2.1. Multivariate regression models
In the US the focus regarding multivariate real estate market forecasting models was
first set on rental adjustment models. These models are constructed according to the
rule that the percentage change of real rents linearly depends on the difference
between the actual and the natural vacancy rates.
The theory of the price adjustment mechanism for rental housing was first
developed by Blank and Winnick (1953) and expanded by Maisel (1963) as well as
Fair (1972). Empirical evidence upon this theory was provided by Smith (1969, 1974)
for Canadian cities and by Rosen and Smith (1983) for 17 different US cities in a
pooled time-series cross-section approach. Gabriel and Nothaft (1988) confirmed this
evidence by using Census Bureau data on 16 US cities. Shilling et al. (1987 and 1992)
and Wheaton and Torto (1988) adopted this framework for the US office market.
This fundamental rental adjustment mechanism is also applied as a core
implication in many multi equation settings. Additionally, in such models the
influence of other exogenous variables such as, for example, demand and supply
indicators is estimated. Prominent work was conducted by Rosen (1984), Hekman
(1985) and Wheaton (1987 and 1999) as well as Wheaton et al. (1997).
Rosen (1984) develops a multi equation model including seven supply and
demand equations. Within his setting he forecasts the stock of office space, the flow of
new office construction, the vacancy rate, and eventually the rent for office space by
using historical San Francisco data from the period of 1961 to 1983. Using OLS,
Rosen shows, among other things, that changes in office rents are inversely related to
6
the deviation of actual vacancies from optimal vacancy rates and directly related to
changes in the overall cost of living.
Hekman (1985) examines the rental price adjustment mechanism and the
investment response in the US office construction market, using data from fourteen
cities over the period of 1979 to 1983. He shows that market rents adjust in response to
local and national economic conditions. On the other hand, investment responds
strongly to rent in a two-stage regression model, and to the long-term growth rate of
office employment.
Wheaton (1987) also focuses on the analysis of the US national market, thereby
concentrating his examination on the appearance of cyclical patterns in real estate
markets. The data from 1967 to 1986 on national office building, construction, and
vacancy show a recurrent ten- to twelve-year cycle. Building up a structural
econometric model for these series capturing the office market offers specific patterns.
On the one hand, there is a quite slow clearing of the market, with an important role of
long-run expectations. On the other hand Wheaton demonstrates that supply is
definitely more responsive to market conditions than demand. Wheaton (1999)
expands this examination and concludes that different types of real estate can have
very different cyclical properties. The different sub-market properties are captured in a
stock-flow model.
Tsolacos et al. (1998) apply this US-literature-based model to the UK office
market. However, they use lagged changes in new office building, in GDP, and in
employment in the banking, finance, and insurance sector instead of vacancy rates to
determine the rental adjustment model. By estimating econometric models for rents,
capital values, and development activity, they show the significant influence of
demand-side economic forces in the user market and the importance of use and
investment market signals in the determination of office building output.
After Corcoran (1987) introduced the concept of equilibrium rents, Hendershott
& Kane (1995), Hendershott (1996) and Hendershott et al. (1999) expanded the
fundamental rental adjustment equation to a linear relation, also incorporating the
deviation from equilibrium rents. Empirical tests were undertaken with US, Sydney
and London office market data, respectively. Hendershott et al. (1999) conclude for
the annual 1977 to 1996 London office market data that rents are mean-reverting.
Furthermore, construction is dependent on lagged values of the positive gap between
actual and the equilibrium net rent. On the other hand, net space absorption is
7
negatively related to rents and positively related to financial services growth.
Additionally, one can see a feedback effect of construction and absorption
developments on rents through their influence on the vacancy rate. Real interest rates
have influence on equilibrium rents, too. The paper infers that the 1985 to 1996 cycle
is highly influenced by the cycle of financial services growth and real interest rates.
Gardiner & Henneberry (1988) follow a reduced form demand-supply approach.
Depending on geographic regions in the UK, they show significant influence of office
space supply and GDP as a demand proxy on office rents. They conclude that this
relation is strongest in booming areas.
Furthermore, Gardiner & Henneberry (1991) extended their model using an
ARIMAX approach based on the assumption of habit persistence and adaptive
expectations in the demand for office space. Permitting GDP as the only exogenous
variable, they also receive good forecasting results for non-booming areas.
Most of the fundamental work on modeling and forecasting real estate market
characteristics presented so far was not conducted according to the latest developments
in econometrics. Throughout the last years several sophisticated econometric tools
have been developed and have become applicable also for real estate market analysis.
More recent work has started to incorporate major improvements as tests for time
series or panel settings on stationarity or cointegration. Some of this work is presented
in the following paragraphs.
Giussani and Tsolacos (1993) analyzed the determination of UK real office rents
by incorporating cointegration analysis. A cointegrated relation between office rents
and the development costs, however, could not be detected. According to Giussani and
Tsolacos (1993) this was mainly because of the short time series available. Continuing
their examination in a dynamic first difference setting, they discovered that changes in
real office rents depend on changes in GDP, lagged changes in banking-financeinsurance employment, lagged changes in property market conditions, lagged changes
in new orders for office buildings, and a measure of uncertainty.
Wheaton & Nechayev (2008) analyze the strong increase in US housing prices
between 1998 and 2005. Estimating a model in levels with several explanatory
economic variables and AR(1) correction as well as working with the same model in
log differences for 59 MSA markets, they show that the growth in fundamentals
produces housing price forecasts far below the actual figures. An examination of the
2005 forecast errors illustrates that price deviations are bigger in larger MSAs,
8
probably due to second home and speculative buying as well as wide spread sub-prime
mortgage market activity. An exact prediction of a slump in house prices cannot be
given.
Hott & Monnin (2008) study fundamental prices in real estate markets.
Therefore, they apply two alternative estimation models. One model is based on a noarbitrage condition between renting and buying. The other model takes the period
costs as the result of market equilibrium between housing demand and supply. Using
quarterly data from 1997 to 2005, the study investigates the USA, the UK, Japan,
Switzerland, and the Netherlands. The authors conclude that actual prices deviate
considerably and for long periods from their estimated fundamental values.
Nevertheless, they also detect evidence for the long run that actual prices tend to return
increasingly to their fundamental values. This is proven by the examination of impulse
response functions and forecast analysis. Eventually, they argue that using the
fundamental price for out-of sample long-term forecasts (greater than three to four
years) significantly improves the precision of the outcomes.
2.2. Univariate models
Besides the application of econometric multivariate forecasting models, univariate
forecasting models such as ARIMA or GARCH models can be also implemented to
predict future rent developments.
McGough & Tsolacos (1995) applied an ARIMA model to obtain a dynamic
structure of the UK commercial property sector real rent. They used the Jones, Lang &
Wootton rental values index (ERV) over the period from the 2nd Quarter 1977 to the
2nd Quarter 1993 to model ARIMA processes for the retail, office, and industrial
sectors. Their specifications were ARIMA(1,2,0), ARIMA(0,2,1), and ARIMA(3,2,0).
Eventually, they conducted a one-step ahead forecast for each sector for the 3rd Quarter
1993. The accuracy of these forecasts is examined by contrasting the predicted values
with the actual rental values of the relevant JLW index figures and shows acceptable
forecasts for the retail, as well as for office rents. The industrial rents’ trend is also
captured however the decrease is overestimated. Several performance measures are
applied to show the deviation of the forecasted from the actual values.
Tse (1997) examines the Hong Kong office and industrial property market by
incorporating quarterly price index data for the period from the 1st quarter 1980 until
the 2nd quarter 1995 for each sector respectively into an ARIMA model. The estimated
processes are ARIMA(2,1,1) for the office sector and for the industrial sector. They
9
are used to forecast each market for the next three quarters. The decrease in office and
industrial property prices by 18.3%, and by 24.6% during the forecasting period is
similar to the actual values. Furthermore, the direction of price changes is as expected.
Performance measures such as the Root Mean Square Error (RMSE) are applied to
show the deviation of the forecasted from the actual values. Theil’s U shows the
model’s forecast performance compared to the naïve performance.
Stevenson (2007) studies the relative accuracy of ARIMA-based forecasts using
quarterly UK office rent data over rolling windows. The author conducts forecasts for
a variety of alternative specifications to figure out the best fitting in-sample model
relative to other alternatives. Moreover, it is shown that conventional measures of fit
such as the Schwartz Bayesian Criterion (SBC) criteria are poor in choosing the model
with the best out-of sample one-year-ahead forecast. Applying previous period models
on the current time window also leads to poor forecasts.
Füss (2007) investigates the US and the UK office, industrial, and retail office
property markets taking a closer look at the quarterly total return data. Similar to
Stevenson (2007), he figures out the best fitting in-sample ARIMA processes per preselected 12-year rolling window selected by information criteria. Furthermore, he
shows results for total return forecasts for the last latest rolling window specification
illustrating much better predictions for the US market. Füss (2007) concludes that
ARIMA models (the same is valid for VAR models) can improve the investor’s timing
however, they should always be combined with other methods such as structural
models and a qualitative assessment.
Crawford & Fratantoni (2003) compare the forecasting performance of ARIMA,
GARCH, and regime-switching specifications, applying quarterly annualized growth
rate data estimated by the US Office of Federal Housing Enterprise Oversight over the
period from 1979 to 2001. The most appropriate GARCH specifications are AR
models – to allow for a constant mean – combined with a GARCH term to account for
time-varying volatility. Depending on the investigated state, the GARCH specification
is substituted by ARCH and EGARCH terms.2 Furthermore, the applied regimeswitching approach shows good in-sample forecasts but inferior out-of sample
forecasts.
The last finding by Crawford & Fratantoni (2003) is challenged by diverse
studies. Miles (2008a), for example, argues that the Markov-switching model is
2
EGARCH accounts for nonlinear dependence in volatility. This will be discussed in chapter 3.3.3 in
more detail.
10
particularly ill-suited to forecasting.3 Therefore, Miles (2008a) applies ARIMA and
GARCH specifications and a GAR model to conduct out-of-sample forecasts. By
using the same data as Crawford & Fratantoni (2003) – extended until the 3rd quarter
of 2005 – Miles (2008a) shows that GAR are superior in markets with the greatest
house price volatility. Nevertheless, in relatively stable markets they do not add much
forecast ability. Miles (2008a) concludes that home price forecasting can benefit
considerably from nonlinear forecasting techniques due to the relatively illiquid nature
of housing markets, and the corresponding boom–bust nature.
Miles (2008b) examines 50 US states regarding GARCH processes. He uses data
from 1979 through the second quarter of 2006. This results in a total of 110
observations. Whereas former studies such as Crawford & Fratantoni (2003) only
detected nationwide GARCH effects, Miles (2008b) concludes that about 50% of the
states under study show GARCH effects. Furthermore he underlines the importance
for portfolio management of accurately capturing GARCH for housing markets.
Miller and Peng (2006) study time variation of single-family home value
appreciation volatility, applying GARCH models among others. Additionally, they
analyze the interactions between the volatility and the economy. Therefore, they apply
quarterly data of 277 MSAs in the U.S. taken from the period of the 1st quarter of 1990
until the 2nd quarter of 2002. Their finding is that for about 17% of the MSAs there is
time varying volatility. They also conclude that the volatility estimated by the GARCH
models is Granger caused by the home appreciation rate and GDP growth rate.
Moreover, the volatility Granger causes the personal income growth rate. However,
the impact is not economically significant.
2.3. VAR and VEC models
In recent years VAR and VEC models which represent combinations of the
characteristics of univariate and multivariate models have been employed more
frequently in the area of real estate market modeling.
Zhou (1997) works on a forecasting model for US single-family housing,
applying monthly data from January 1970 to December 1994. The author therefore
takes a closer look at the two non-stationary series sales and price. Zhou (1997) further
shows the existence of a cointegrating vector, demanding an error correction term
within his VAR setting. Testing for Granger causality, it is shown that price affects
3
For further evidence refer to Bessec and Bouabdallah (2005).
11
sales significantly however sales affect price only weakly. Using only the 1970 to
1990 data for model specification, a well-suited out-of-sample forecast for the period
until 1994 is conducted.
Hendershott et al. (2002) examine the UK retail and office market, basing their
VEC model on (annual) panel data covering 11 regions over 29 years. Estimating
separate regional models, they also combine regions on the basis of income and price
elasticities in the long-run and short-run models. Considering stationarity and
cointegration, they model rents dependent on the two variables consumer expenditures
and floor space plus floor space under construction for the retail market and dependent
on finance and business services employment as well as floor space plus floor space
under construction for the office market. The error correction term is interpreted as the
missing lagged vacancy rate. For the retail market the first difference equation is also
estimated with the first lag of rents as a dependent variable significantly increasing the
R² at least for the London area. The authors’ interpretation is a far more rapid rent
adjustment to shocks in the London area than in other regions. For the office market it
is remarkable that although supply is highly significant for the long-run estimation, the
first difference rents in the short-run model are only dependent on finance and
business services employment, whereas the supply coefficient is insignificant.
An interesting view on the assumption of cointegrating relations in the housing
market is provided by Gallin (2006). He contradicts the common assumption of
cointegration broadly found in the literature by showing that house prices and income,
at least for his panel data setting of 95 US metropolitan areas over 23 years, are not
cointegrated. He refers to the greater power of panel cointegration tests compared to
common time series cointegration tests and argues that, for example, Malpezzi (1999)
applied wrong test specifications. He concludes that error correction specifications for
house price and income might be misleading and may even show spurious results and
thus leading to highly deceptive forecasts.
Stevenson (2008) investigates the Irish residential property market, using
quarterly data for the period 1978 until 2003, including the price boom era during the
last years of the period. Besides the application of different modeling approaches, an
error correction framework similar to Malpezzi (1999) is also included, leading to
more consistent and robust findings. Stevenson (2008) concludes that a considerable
premium over fundamental values grew in the Irish market during late 1990s, reaching
a peak in 1999 and 2000. Nevertheless, prices have largely been in line again with
fundamentals throughout the sample period’s most recent years.
12
3.
Theoretical Foundations
In this chapter I start with a discussion of the theoretical foundations of the real estate
market which are important to understanding the characteristics of rent and total yield
developments. Furthermore, in subchapter 3.2 I show statistical specifics which have
to be considered with time series and panel data. This is followed by a discussion and
evaluation of the theoretical fundamentals of the applied models in subchapter 3.3.
Finally, subchapter 3.4 gives an overview of forecasting techniques and an analysis of
forecasting performance measures.
3.1. General real estate market characteristics
In this subchapter I will discuss some characteristics of real estate markets which are
crucial to understanding the process of rent and total yield developments in specific
cities. Therefore, I first give a definition of the term real estate, followed by a
presentation of possible segmentations of the real estate market, focusing in detail on
the four quadrant model of DiPasquale and Wheaton. This model already gives insight
into the mechanisms of the real estate market. The subchapter closes with a brief
discussion of important real estate specifics.
3.1.1. Definiton of the terms real estate and real estate market
The term real estate can be defined from three different perspectives. According to, for
instance, Geltner, Miller, Clayton, and Eichholtz (2007, p. XXI), one has to distinguish
between the physical, the legal, and the financial economic view. The physical
“Bricks-and-Mortar Concept” defines real estate as a three dimensional structure of
walls, ceilings, and floors. However, as Schulte et al. (2000, p. 16) state, this definition
does not consider aspects of the underlying parcel. From the legal point of view, real
estate can only be regarded as a building, stationary and fixed at a certain location, in
combination with a parcel and the assigned rights. The building cannot be considered
autonomous. This view is widely shared throughout many jurisdictions.4 According to,
for instance, Schäfers (1997, p. 14 ff.), the economic definition focuses on real estate,
on the one hand, as a factor of production. On the other hand, it is seen as real or
capital investment, where investors focus on the asset’s potential future cash flow.
4
See, for instance, for Germany §93 ff., § 873 and § 902 BGB, for Switzerland § 655 Abs. 2 and §
943 Abs. 1 ZGB.
13
In a next step, real estate can be categorized according to its occupancy. One can
differentiate between residential, commercial, and special property. Commercial
property contains office buildings, shopping centers and industrial property. Special
properties are, for example, cinemas, hotels, power stations, etc.
This differentiation and the implied heterogeneity constitute the existence of
certain real estate markets concerning occupancy. According to Geltner, Miller,
Clayton, and Eichholtz (2007), the term real estate market can be defined as a
mechanism where real estate is voluntarily exchanged among different owners.
However, real estate markets cannot only be subdivided into residential, office, or
special property markets. Several further approaches to capture all facets of real estate
markets have been developed.
According to Dopfer (2000, p.22) and Kofner (2004, p.22 f.), real estate markets
can be subdivided with reference to regional borders. This approach is based on the
immobility of real estate supply in the short run. Since short-run supply cannot adapt
to changes in demand in a particular area, the real estate market in this area can
develop differently compared to other ones. Thus, one can talk about regional real
estate markets. Gantenbein (1999, p. 35 f.) chooses a different approach when he
distinguishes between a primary market, where real estate inventory is extended and
reduced, a secondary market, where real estate is traded, and a rental market, where
market rents are determined. Another segmentation has been introduced by DiPasquale
and Wheaton (1992). This approach is outlined in more detail in the following
subchapter.
3.1.2. The four quadrant model according to DiPasquale and Wheaton
In their widely recognized paper, DiPasquale and Wheaton (1992) subdivided the
general5 real estate market into two major categories. On the one hand, they identify
the market for real estate space and on the other hand they present the market for real
estate assets. Afterward, they show their prominent four quadrant model, which
explains the important connections between these two markets and how they are
affected by financial markets and macroeconomic influences. It shows in detail the
implications from exogenous shocks on rents, asset prices, construction, and the stock
of real estate.
5
The outlined model is valid for all submarkets segmented according to occupancy such as residential,
commercial, and special property markets
14
In the market for real estate space, tenants and the type and quality of the
available buildings define the rent. At the same time the price of space is determined
by investors who trade the underlying buildings in the asset market. Rent as well as
price level is positively influenced by positive demand shocks and negatively affected
by negative demand shocks and positive supply shocks. Thus, new supply depends on
the relation between the market price of the asset and its replacement costs. Although
both prices are supposed to be the same in the long run, short-run deviations might
appear. This can happen due to lags in the construction process. For instance, if the
market faces a positive demand shock, the market prices will rise and hence move
above the construction costs. This will motivate new construction. However, until the
newly created supply can enter the market on average some three to five years have
gone by. Ceteris paribus, after this time lag the prices will be equal again. This
example illustrates the cyclical nature of the real estate market.6
The interaction of the real estate space and the real estate asset market can be
found at two points. The first is rent and the second is construction. Whereas, rent is
determined in the space market, it has influences on the asset market, since it
represents the current and future income stream for investors. On the other hand, new
construction, which means asset increase does not only lead to decreasing prices
ceteris paribus. It also sets pressure on the rents in the space market, which are
declining as well.
Graph 1 illustrates the prominent four quadrant model. Here, the two submarkets,
real estate space market and real estate asset market, are depicted as follows. The two
quadrants on the right represent the space market. The two left quadrants describe the
asset market. The top right quadrant's axes are rent7 and stock of space.8 Within this
quadrant the rents are determined in the short run and thus the demand for space,
which is represented by the line. In equilibrium, the demand for space, D, is equal to
the stock of space, S. According to graph 1, rent, R, must be determined in a way that
the demand is precisely the same as the stock, taking the stock as given. Thus, D is a
function of R and the economic conditions, as can be seen in equation 1.
Equation 1: D( R, Economy ) S
6
The cyclicality of the real estate market is discussed in more detail in chapter 3.1.3.
7
Per unit of space.
8
This is also measured in units of space such as square feet.
15
Graph 1: Four-quadrant model
Asset Market:
Valuation
P
Property Market:
Rent Determination
Rent
R
i
D ( R , Economy )
S
Price
'S
P = CCosts = f(C)
Asset Market:
Construction
Construction (sq ft)
C dS
Property Market:
Stock Adjustment
The top left quadrant of graph 1 illustrates the rent to price ratio and thus the
capitalization rate for real estate assets represented by the ray from the origin. It is the
first part of the asset market with two axes: rent and price.9 This capitalization rate
presents the current yield that investors require to invest in real estate assets. It is
determined by four influences: the long-term interest rate in the economy, the expected
growth in rents, the risks associated with that rental income stream, and the treatment
of real estate in the respective federal tax code. The higher the capitalization rate is,
the more the ray turns to the upper right. Furthermore, the capitalization rate is taken
as exogenous in this quadrant. Consequently, the price for real estate assets, P, is
determined by the ratio of rent level, R, which is taken from the top right quadrant and
the capitalization rate i.
Equation 2: P
9
Per unit of space
R
i
16
The bottom left quadrant determines the construction of new assets. The two axes
are price and construction10. In this part of the asset market curve, f(C) represents the
replacement cost, CCosts, of real estate. The cost of construction is expected to rise
with greater building activity. For that reason, the curve moves to the bottom left
direction. It cuts the price axis at a point that determines the minimum value necessary
for basic construction. The line is more vertical, the more the construction can be done
at the same costs regardless of the actual level of construction in the market. The price
and the construction costs of real estate must be equal, since both are a function of the
construction level, C.
Equation 3: P = CCosts = f(C)
The bottom right quadrant again represents the real estate space market with the
axis: construction and stock. Here, the annual flow of new construction is transformed
into the long-run stock of real estate space. The change in stock, 'S , depicts the new
construction in a given period reduced by the depreciation (removal) rate, d.
Equation 4: 'S C dS
Here, the ray deriving from the origin demonstrates the level of the stock that has
to be built to keep the long-run stock constant. As a result, 'S equals zero and S
C
.
d
The total system is in equilibrium when the starting and end value of the stock
are the same. If they are not, an adjustment process according to the described
mechanisms starts.11
Concluding, the DiPasquale & Wheaton four quadrant model shows the
relationship between the two submarkets and the implications of market mechanisms
on the total real estate market. Model-inherent demand and supply variables are
examined and their influence on as well as their interrelations with other variables are
analyzed. Since it is a very general approach the model also works for the several
submarkets subdivided according to occupancy such as the office market, which is the
object of the empirical part of this work.
As described previously, the model is a long-run equilibrium model allowing for
short run deviations, which can be simulated by exogenous shocks and thus by shifts
of the lines within the model. These shocks and especially the real-estate-specific
10
11
In square feet.
DiPasquale & Wheaton (1992) and especially the textbook DiPasquale & Wheaton (1996) offer
detailed insight into possible shocks and comparative statics. The interested reader is referred to them.
17
adjustment process after the shocks already shed light on real estate particularities that
are discussed in the subsequent subchapter.
3.1.3. Real estate market characteristics
As the last subchapters have already noted, real estate markets, including office real
estate markets, have some specifics that distinguish them from other economic
markets. Among these specifics are:12
x Market inefficiencies such as
o Immobility
Real estate is immobile. It is irremovably connected with its original location.
o Heterogeneity
Every piece of real estate is individual regarding location, architecture,
occupancy, age, etc. Thus, real estate is an economic good that has little
comparability and, consequently, limited market transparency. This is one reason
for the low market liquidity.
o High transaction costs
Another reason for relative market illiquidity is high transaction costs. Due to
lack of transparency, there are high information costs leading to high real estate
broker costs. Furthermore, there are taxes and notary fees when a transaction is
determined and executed. These costs also explain the longevity of the real estate
investment horizon.
o Illiquidity
Real estate markets are relatively illiquid. The main reasons are their
heterogeneous character and the high transaction costs. This illiquidity, among
others things, constitutes the booms and busts of the real estate markets.
x Cycles, determined by
o Economic influences
The real estate market and especially the office market are dependent on the
economy. A positive economic development as measured, for instance, by a
12
This overview covers the most important specifics and it is based on Gantenbein (1999, p. 34 f.),
Chinloy (1988, p. 13 f.), and Schulte et al. (2000, p 18 ff.).
18
GDP increase also has a positive influence on the demand for office space. The
outcome of this demand can, for instance, be represented by a change in its proxy
office employees.
o Length of the construction process
On average, it takes two to five years from the planning to the completion of a
real estate project. Thus, after a positive demand shock, one can observe a time
lag until the demanded new office space eventually enters the market. These
coherences underlie the cyclical behavior of the real estate market, leading to
fluctuations in rent or price as well as vacancy levels.
A simplified illustration of the real estate cycle can be found in the Jones Lang
LaSalle office clock, which depicts the current stage of the real estate cycle in a certain
city according to the current office rent development.13 More details and a
comprehensive literature overview of real estate cycles is provided in Pyhrr and Born
(1999).14
These specifics illustrate that the market for real estate is not very efficient.
Literature assigns weak efficiency towards real estate markets.15 On the other hand,
this implies the possibility of forecasting, at least partially, the time path of real estate
rents, prices, or yields. Case and Schiller (1989) were the first to demonstrate this for
the US housing market.
3.2. Specifics of time series and panel data
In this subchapter I am going to talk about important characteristics of time series and
panel data. After a definition and brief discussion of both terms, I therefore focus on
the explanation of stationarity and cointegration. Both concepts have to be understood,
since they are important prerequisites to correctly transforming a time series and
constructing sophisticated forecasting models.
13
The office clock is published in major newspapers. The latest developments can be noticed on
http://www.joneslanglasalle.com/Pages/Research.aspx.
14
Also refer to Mueller, Pyhrr & Born (1999) as well as Grissom & DeLisle (1999).
15
Refer, for instance, to Guirgius (2005).
19
3.2.1. Definition of time series data
In general, we distinguish between time series and cross sectional data. Whereas the
latter is composed of variable observations of firms, countries, households, cities, etc.
at a fixed point in time, time series data consists of data samples on variables over
time, as, for example, the rent development in a certain unit from 1975 until 2006. It is
important to state that in time series data, unlike in cross sectional data, the
chronological ordering of observations reveals vital information. This, however,
implies additional difficulties for the statistical analysis, since most economic or realestate-related time series data points are not independent of their predecessor. Another
phenomenon observed with time series data is seasonality, which mainly appears when
the data frequency is recorded in a high order, such as, for instance, daily, weekly,
monthly or quarterly. Furthermore, especially in economic time series, cyclicality can
be experienced.16
3.2.2. Definition of panel data
Panel data is a combination of cross sectional and time series data. This means that for
each cross sectional unit - city, firm, individuals, etc. - all variables are observed over
time. For instance, all analyzed variables for each city such as rent, office employees,
office space inventory, etc. are collected from 1992 until 2006. It is important to note
that the observations over time have to come from the same cross sectional unit. If the
combined series do show a certain length, the same difficulties regarding
independence of the observations in time as with single time series data can appear. A
further special characteristic of panel data is the opportunity to deal with unobserved
effects. Cross sectional unit time-independent specific effects such as gender or a city's
distance to the next airport, which could lead to biased and inconsistent estimators of
the parameters of the further variables in a model, can be eliminated by techniques like
first differencing or cross sectional fixed effects estimation. Since real estate markets
are very heterogeneous these techniques can be especially useful in establishing
efficient forecasting models. To deal with unobserved effects implying different
averages of the dependent variable over time, period fixed effects estimation is
applicable.17
16
For a more detailed discussion on time series data refer for instance to Wooldridge (2009,
p. 340 ff.).
17
For a more detailed discussion of panel data and fixed effects estimation, refer, for instance, to
Wooldridge (2002, p. 247 ff.).
20
3.2.3. Stationarity
A time series is called stationary or integrated when the probability distributions of the
underlying process are stable over time.18 However, if, for example, the process
exhibits trending behavior the mean of the series changes over time and one
requirement for stationarity is violated. This can lead to spurious regressions, i.e.,
inefficient parameter estimates, followed by suboptimal forecasts based on the
estimated equation and invalid significance tests concerning the parameters according
to Granger & Newbold (1974). Moreover, a stationary process implies simplified
statements regarding the law of large numbers and the central limit theorem.
For time series modeling it is sufficient if the underlying process is weak or
covariance stationary. Weak stationarity concentrates only on the first two moments of
the underlying process. Mean and variance have to be constant over time.
Additionally, the covariance has to be independent of the initial point in time and is
only dependent on the distance between the two terms.
Throughout the last several decades, many tests, called unit root tests, have been
developed to examine time series regarding stationarity. Fuller (1976) as well as
Dickey and Fuller (1979) and Dickey and Fuller (1981) were the pioneers. The
Dickey-Fuller as well as the Augmented Dickey-Fuller test found recognition and
application. The same is true for the Phillips-Perron test introduced by Phillips and
Perron (1988). The Augmented Dickey-Fuller test and the Phillips-Perron test are both
applied also within the empirical part of this work. In addition to these tests, many
further procedures have been developed. A good overview is given in Kirchgässner
(2007, p. 163 ff.).
The test procedures mentioned thus far work well for simple time series data.
However, recent literature proposes extended tests when panel data has to be checked
for stationarity. Choi (2001), among others, developed a procedure on the basis of the
original Phillips-Perron test. The second test procedure applied in the empirical part of
this work is taken from Hadri (2000).
If a time series is detected to be non-stationary, for instance, if a trend is
discovered within a time series, we have to detrend the series to reach stationarity.
This can be done by taking the difference of every value in the time series with its
18
This definition is taken from Wooldridge (2009, p. 377 ff.).
21
predecessor. This approach is repeated until the transformed time series is stationary.
Another opportunity would be to regress on a time trend.19
3.2.4. Cointegration
Two times series are called cointegrated if they are non-stationary in their levels, but
stationary when first differenced, thus if they both are integrated of order 1, and if
there at the same time exists a parameter which generates a stationary process when
both level series are set into a linear combination. This parameter is called the
cointegrating parameter.20 The idea of cointegration was first introduced by Granger
(1981) and extended by Granger (1986). The first methodologically formatted paper
was published by Engle and Granger in 1987.
If two or more variables are cointegrated, there are economic implications. It
means that these variables have a long-run relationship. For instance, it is widely
recognized that the non-stationary series of income and consumption have such a longrun relationship. This implies that if income increases, consumption will do the same
on average. In the short run, one might observe deviations from this pattern, but in the
long run cointegration leads to a very similar development of both series. So-called
error correction models have been developed which consist of both a long- and a shortrun relationship to depict and estimate these coherences.21
It can be tested whether two or more time series are cointegrated. Along with
several other tests that have been developed, the procedure based on Johansen and
Juselius (1990), Johansen (1991) and Johansen (1995) is widely accepted. The same is
true for the approach introduced by Lütkepohl and Saikkonen (2000) and Saikkonen
and Lütkepohl (2000). A cointegration test procedure for panel data was created by
Pedroni (1999), Pedroni (2001) and Pedroni (2004). Banerjee (1999) gives a good
overview of the topic.
3.3. Theoretical fundamentals of common forecasting models
As we could see in the discussion in chapter 3.1, real estate markets, including office
real estate markets, have some special characteristics compared to other asset markets.
19
For more details refer for instance to Kirchgässner (2007, p. 159 ff.).
20
This definition is taken from Wooldridge (2009, p. 637 ff.).
21
In this context chapter 3.3.4 shows the example of a vector error correction model in more detail.
22
In particular, the specifics of market illiquidity and market cyclicality imply
autocorrelation and possibly volatility cluster in the underlying series, which have to
be considered when establishing and choosing forecasting models.
Thus, in the following subchapters, I present the most prominent types of models
which can be applied in real estate variable forecasting. Therefore, I examine
econometric- and time series models as well as combinations of these fundamental
models. For each model I start with a brief general overview. I subsequently talk about
the model’s specifics and how it is constructed with regard to the techniques discussed
in chapter 3.2. Based on the characteristics presented, I conclude this subchapter with a
recommendation when and how to apply each model.
3.3.1. Multivariate regression model
The target of econometric models is to estimate the relationship between economic
variables which are supposed to be linked due to economic theory. These
mathematical models, or mathematical representations, of the relation of the included
variables are therefore tested for statistical significance. In other words, it is shown
whether the implemented model is sophisticated enough to display a precise
replication of the relation in reality, which is the technical prerequisite to run forecasts.
The first econometric model was constructed by Tinbergen (1939) for the United
States.
In econometric models the relations between the implemented economic
variables are expressed in an equation or in a system of equations. These equations can
cover different kinds of functions, linear or non-linear. Since most of the applied
regression functions in the relevant literature are linear and since in the multivariate
empirical investigation of this work I focus on the application of single equation linear
regression models, I will focus on them in the further theoretical discussion. The
classical linear regression model has four assumptions:22
x Linearity of the relationship between dependent and independent variables
x Independence of the errors (no serial correlation)
22
The classical linear regression model and its assumptions and extensions can be studied in detail in
every basic regression textbook such as, for instance, Wooldridge (2009), Brooks (2005) or Gujarati
(2003). Often non-linear relations of economic variables are transformed into linear ones. For a more
detailed discussion refer to, for example, Greene (2003, p. 165 f.).
23
x Homoskedasticity (constant variance) of the errors
o versus time
o versus the predictions (or versus any independent variable)
x Normality of the error distribution.
Equation 5 illustrates the general form of a multivariate single equation model.
Equation 5: y
f ( x1 , x2 , x3 ,..., xn )
This model represents the relation between an endogenous variable y and the
exogenous variables xi . The endogenous variable is dependent on the exogenous
variables and thus is explained by the regression model. On the other hand, the
exogenous variables are independent and serve to describe the endogenous variable.
To identify exogenous, for example, explanatory variables for the endogenous
variable, one should first consult economic theory and the proposed relationships. On
this basis a correlation analysis between the endogenous and each potentially
exogenous variable demonstrates the statistical significance of each relationship. As a
next step, the linear regression model can be constructed by implementing all
reasonable and significantly influencing exogenous linearized variables. Then, the
exact relation between the endogenous and exogenous variables included in this
regression model has to be estimated. According to Equation 6, presenting the classical
multivariate linear regression equation, parameters D i reflect the marginal influence of
variable xi on y. C denotes a constant and H i the error term.
n
Equation 6: y
c ¦ D i xi H i
i 1
Prominent examples for estimation techniques to deliver reasonable values of D i
are Ordinary Least Squares (OLS) or Maximum Likelihood. The first approach is also
applied within this work. Here, the parameters D i are estimated in such a way that the
sum of the squared deviations of the forecasted from the actually observed values of
the endogenous variable is minimized. To receive asymptotical normal distribution in
the residuals and thus efficient estimates at least 30 observations for each variable
have to be available. On the other hand, Maximum Likelihood draws samples out of a
population. Then the parameters D i are estimated in such a way that the probability of
their realization throughout the samples is maximized.
24
If time series or panel data are applied, the model can furthermore be expanded
by time lag structures. Lags of the dependent variable can be included if it increases
the explanatory power of the model. It is also possible to enter independent variables
with a certain lag.23 When applying time series or panel data, autocorrelation in the
residuals can appear, violating the classical regression model assumption that demands
independence of the residuals. And since real estate rent, price, or total yield series are
typically autocorrelated, this can lead to biased estimations and test results of
econometric models. For the general economic time series case, this was first detected
by Cochrane & Orcutt, who also found a way to eliminate first order autocorrelation
by transformation.24 This approach is also undertaken within the empirical part of this
work. Equations 7 and 7a show the adjusted linear regression model.
n
Equation 7: yt
c ¦ D i xi ,t H t
i 1
Equation 7a: H t
UH t 1 Q t
3.3.2. ARIMA model
Unlike the classical regression model, Autoregressive Integrated Moving Average
models (ARIMA) are not based on the causal relationship between endogenous and
exogenous variables. They describe the development of the explained variable through
its own past values and without considering exogenous influences. Thus, the ARIMA
approach is a univariate approach. Contrary to the multivariate regression models,
ARIMA models are not dependent on economic theory. Thus, their application is
favorable when exogenous variables cannot be observed, applicable time series do not
exist, or no theory exists at all.
The ARIMA model, first presented by Box & Jenkins (1970), has the basic assumption
that the past development of a certain time series also continues into the future. Here,
the variable’s development over time is considered a stochastic process dependent on
random influences. Equation 8 depicts a representation of an Autoregressive Moving
Average ARMA(p,q) process.
23
However, one has to consider that it is not possible to enter an independent variable twice or more
often with different lag structure on the right hand side of the equation, since this violates the linear
regression prerequisite of strict exogeneity.
24
For details refer to Cochrane & Orcutt (1949). A slightly different approach is applied by Prais &
Winsten (1954).
25
Equation 8: yt
p
q
i 1
i 0
G ¦ D i yt i H t ¦ EiH t i
The model can be perceived as a linear regression where the lagged values of the
variable and its past residuals are the exogenous variables.
An ARMA(p,q) process consists of two components: the autoregressive process
(AR(p)) and the moving average process (MA(q)). The AR process, which is depicted
by the first part of equation 8, determines the predicted value of yt as the weighted
sum of its own lagged values.25 Furthermore, random events can influence the time
series. Past random events are implemented by the MA processes shown in the second
part of the equation. The order of the process shows how many earlier observations of
the variable demonstrate influence on the predicted value and hence, how many factors
have to be incorporated into the model. In general, AR(p) and MA(q) processes can
constitute forecasting models on their own. Besides ARIMA(p,d,q) models, the
empirical part of this work also applies the single processes for certain cities and time
periods.
A prerequisite for the application of ARMA models is weak stationarity of the
underlying time series. However, many time series, as can also be recognized in the
empirical part of this work, are non-stationary by showing, for instance, a linear trend.
According to chapter 3.2.3 this is no problem as long these time series can be
transformed into stationary ones by, for instance, taking the first differences. If a time
series has to be differenced d-times to become stationary, the series can be represented
as an ARIMA(p,d,q) process, where the I stands for integrated denoting the kind of
transformation the underlying time series faces.
Another requirement when applying ARMA models for forecasting is the
invertibility of the included MA(q) processes. Invertibilty has to be accomplished to
receive a unique parameterization. It is defined as E 1 .
The determination and construction of ARIMA models can be done in different
ways. One way is to start with the identification of the process, which means
discovering the parameters p, d, and q. To decide on the degree of integration d, one
can apply several unit root tests such as the Augmented Dickey-Fuller or the PhillipsPerron test.26 Then order p and q are estimated according to the autocorrelation and
25
G represents a constant term.
26
These tests and other important time series specifics are discussed in more detail in subchapter 3.2.3.
26
partial autocorrelation function.27 Thus, the best process has been determined. After
this step, the model parameters are estimated. If the model is stationary, the chosen
parameters are significantly different from zero, and the residuals are independent of
each other, the model is said to be well specified.
A different way is to first construct many different models, estimate their
parameters and determine in a second step the best fitting one via the application of
several performance measures.28 For efficient parameter estimation, the time series has
to consist of at least 30 observations.29
3.3.3. GARCH model
The multivariate regression and ARIMA models examined thus far apply the
conditional expectation to represent the mean development of the time series. To come
up with the best fitting forecast, they only present the conditional mean. This is done
under the prerequisite that the variance of the forecast errors will be minimized and
under the assumption that, on the one hand, the residuals are uncorrelated and, on the
other hand, homoskedastic.
Nevertheless, times of high volatility interchanged with times of low volatility
have been found throughout many economic and financial time series. Some of the
literature has also determined this condition for real estate time series.30 Mandelbrot
(1963) was the first to show that financial market data has fatter tails than normal
distribution would allow, leading to leptokurtic distributions. Hence, for these series
one cannot talk about a constant variance or homoskedasticity of the residuals, but one
can observe volatility cluster. Since in this case assuming constant residual volatility
for these series would deliver inefficient parameter estimates and underestimate the
actual risk, Engle (1982) illustrated and applied the residual variance as a function of
its own past. Thus, here the variance is modelled as an AR(q) process, with q denoting
the order of the process. The overall model is called autoregressive conditional
heteroskedasticity model or ARCH(q). Equation 9 represents an ARMA(p,q) model to
27
For a more detailed guidance refer to Kirchgässner (2007, p. 67).
28
Furthermore, a combination is possible by pre-selecting different ARIMA processes due to
autocorrelation as well as partial autocorrelation function and then applying the performance measures
for the estimated models. Regardless, the time series has to be made stationary in the very first step.
29
This can be surveyed in Weiss & Andersen (1984). However, the literature also shows different
opinions. Beumer (1994) wants at least 20 observations, whereas on the other hand McGough &
Tsolacos (1995) demand 50.
30
For details refer to chapter 2.2.
27
estimate the conditional mean. The construction and estimation procedure is the same
as the one described in chapter 3.3.2.
Equation 9: yt
p
q
i 1
i 0
G ¦ D i yt i H t ¦ E iH t i
Equation 9a: ht
E[H t 2 ]
Equation 9b: ht
a0 ¦ aiH t i 2
q
i 1
Equation 9b shows the conditional variance in an AR(q) representation, with ht
denoting the conditional variance and H t 2 denoting the unconditional variance. a0 ! 0
and ai ! 0 are prerequisites to always keeping the conditional variance positive. Order
q can be determined with an ARCH LM-test31 or according to the autocorrelation and
partial autocorrelation function of the squared residuals.
Bollerslev (1986) introduced the generalized autoregressive conditional
heteroskedasticity (GARCH) model. Unlike the ARCH model, here, the conditional
variance is estimated as an ARMA(n,p), and not only as an AR(q) process. Here, more
parsimonious parameterization is accomplished. A GARCH(p,q) model can be
illustrated in three equations. Equation 10 represents an ARMA(p,q) model to estimate
the conditional mean. Again, the construction and estimation procedure is the same as
the one described in chapter 3.3.2.
Equation 10: yt
p
q
i 1
i 0
G ¦ D i yt i H t ¦ EiH t i
0,5
Equation 10a: H t
vt ht
Equation 10b: ht
a 0 ¦ a i H t i ¦ E ht i
q
i 1
2
p
i 1
Equation 10b shows the conditional variance in an ARMA(n,p) representation,
with ht denoting the conditional variance and H t 2 denoting the unconditional variance.
These approaches were extended after their original development. For instance,
since in financial markets one can observe a leverage effect signifying a higher
31
For a detailed discussion of a Lagrange multiplier (LM) test for autoregressive conditional
heteroskedasticity, refer to Engle (1982).
28
volatility as a consequence of negative shocks compared to positive shocks, Glosten,
Jagannathan, and Runkle (1993) implemented different GARCH models for positive
and negative shocks. This new model is called threshold autoregressive conditional
heteroskedasticity (TARCH). A further problem arises when one estimates higher
order ARCH models without restrictions, since the estimated coefficients break the
non-negativity
constraints.
The
exponential
autoregressive
conditional
heteroskedasticity (EGARCH) model developed by Nelson (1991) solves this problem
by ensuring that the conditional variance is always positive, and furthermore, it
considers the above-mentioned asymmetry between positive and negative shocks.
Moreover, the ARCH-in-mean (ARCH-M) model regards the assumption that higher
risks usually imply higher returns, leading to a cadence of mean and variance. This
approach was developed by Engle, Lilien, and Robins (1987).
3.3.4. VAR and VEC models
Vector Autoregressive Systems (VAR) were first developed by Sims (1980) as a
substitute for systems of simultaneous equations. Sims argued that in this system all
variables depend on all other ones, i.e. all variables in this system are endogenous.
Thus, the traditional structural form of an econometric model based on economic
theory is no longer identifiable and moreover no longer necessary. This is the case
since, according to an individual's rational expectations, almost all variables have
some relationship with all other variables of a system and all restrictions, as are
inherent in a traditional structural form, are implausible. Sims illustrates his arguments
with a commodity example. He assigns the biggest influence on the coffee world
market price to the Brazilian coffee harvest and its market entry in autumn. Surely a
persistent frost in spring will destroy a significant part of the Brazilian coffee harvest,
and thus will lead to a supply reduction in autumn. This again is supposed to lead to
higher prices. Regardless, there should be no influence on the demand function.
However, if consumers are aware of the Brazilian spring time weather conditions, it is
not improbable that they will purchase extra coffee to enlarge their stock at the current
low prices. Consequently, the weather in Brazil not only influences the coffee supply
but is also a determinant of the coffee demand.
Equation 11 depicts the representation of a VAR(p) system.
p
Equation 11: Yt
G ¦ AY
i t i (t
i 1
29
with Ai as the k-dimensional quadratic matrices and E as the k-dimensional
quadratic vector of the residuals at time t. G is the vector of constant terms. Yt
represents the variables of the system, which are all endogenous, as already clarified
above. All Yt , on the one hand, depend on their own lagged values. On the other hand,
they depend on the lagged values of all other Yt in the system. Yt could be every
variable.32 Yet, the implementation of every additional variable and its particular lags
and their estimations has to be set regarding the number of available observations.33
Since VAR(p) models are over-parameterized systems, their individual
parameters can barely be construed. The adoption of impulse response analysis can
however ease this problem. In this context, a shock to a certain variable does not only
influence this variable directly. Furthermore, it is also forwarded to the other
endogenous variables through the dynamic structure of the VAR. The impulse
response function shows the effect of this shock toward current and future values of all
endogenous variables.34
A further requirement is the stationarity of each single series. Only if all included
variables are stationary in the weak form, is the system stable. Thus, the system leads
to meaningful forecasts. If the series are not stationary, they have to be differenced dtimes until stationarity in all series is accomplished. Then the VAR model has to be
constructed in the respective differenced form. However, for a system where all level
series are non-stationary yet cointegrated, a Vector Error Correction Model (VECM)
can be applied. A VECM is represented as a VAR with an additional error correction
term. Equation 12 presents a VECM(p).
p 1
Equation 12: 'Yt
G OYt 1 ¦ Ai 'Yt i (t
i 1
O b ˜ c , c is the cointegrating vector. The relation c ˜ Yt
d depicts the underlying
economic coherences and b represents an adjustment coefficient to return to the
32
On the one hand, this atheoretical approach has been met with a lot of criticism. On the other hand,
the development of structured VARs can serve to mitigate it. Here, reduced forms of VARs are
constructed according to an underlying idea or theory. For more details refer to Hamilton (1994, p.
324 ff.).
33
For the determination of the optimal lag length in a VAR(p) system several test procedures can be
applied such as, for instance, the Akaike information criterion or the Schwartz information criterion.
For a detailed discussion refer to Lütkepohl (1991), section 4.3.
34
Variance decomposition or Granger causality are two further ways to clearly determine the relations
and causalities between the variables employed. For details refer to Hamilton (1994, p. 323) or to
Granger (1969).
30
economic equilibrium. This model can now capture long-run convergence between the
variables as well as short-run dynamics. General error correction models were first
introduced by Sargan (1962) and popularized by Davidson et al (1978). Later they
were applied to the vector setting.
3.3.5. Evaluation of the examined forecasting models
All models theoretically examined in subchapter 3.3 operate well with time series data.
However, when the data base is given in a panel setting, only multivariate regression,
VAR, and VEC models are applicable. The minimum of necessary observations for the
employed time series strongly depends on the number of explanatory variables
implemented and thus on the number of parameters which have to be estimated.
Nevertheless, for estimations of multivariate regression or ARIMA models at least 30
observations have to be available. For ARCH models more observations are required
on average due to the fact that additional parameters appear in the conditional variance
equation. The advantage of GARCH models on the other hand is that the modeling of
the dependencies between the squared residuals such as ARMA processes results in a
more parsimonious parameterization and thus less required observations on average
compared to the ARCH setting. VAR models require a great deal of observations. This
is the case since each additional included variable enriches the system by one more
equation. Furthermore, one has to consider the fact that the longer the lag length, the
more parameters have to be estimated. The data demand of the VEC models is similar.
Moreover, one also has to consider the supplementary error correction term here.
All models have in common that they can display the cyclical pattern that
appears in real-estate-related time series. Thus, they are able to recognize extrema and
turning points in the data. Additionally, exogenous variables are included in
multivariate regression, VAR, and VEC models to explain the endogenous series. On
the other hand, ARIMA and GARCH models only consider information from past
values of the examined variable. Therefore, they are considered rather technical
models without relation to economic theory. The same criticism is given to VAR and
VEC models since these are assuming dependencies between all included variables in
all directions.35
35
This is mitigated through the structural VAR approach, where variables are included regarding an
underlying theory. VEC models can also be subsumed to have theoretical background since theories of
long- and short-run relations of the implied variables can be tested.
31
The phenomenon of autocorrelation in the residuals can be resolved in
multivariate regression analysis to receive efficient estimates. All other models are
based on the fact that past values of the examined endogenous variable are used to
explain the variable itself. Autocorrelation is exploited to present efficient estimates.
Furthermore, GARCH models are the only models that consider altering volatility and
thus can cope with volatility clusters.
An examination of the models regarding forecasting performance for different
forecasting periods shows a pattern of superiority of time series approaches compared
to the multivariate model approach. Granger and Newbold (1975) showed that for the
short term the time series approach created significantly better forecasts than
multivariate models that sometimes consisted of over a hundred equations. Yet, the
opposite is true for the longer run. According to Tse (1997), ARIMA models perform
well up to the forecasting of four periods. However, referring to Huber (2000, p. 142),
with an increasing forecasting horizon, the forecasting error also increases due to the
ARIMA-model-inherent fact that forecasted values converge to the mean of the
observed series in the long run. This problem does not appear for multivariate
regression models.36
Thus, one can conclude that time series models work in a superior manner when
the forecasting period is short, while multivariate models are better in the longer term.
Nevertheless, one has to consider that multivariate models imply conditional forecasts.
This means that dependent on the lags of the exogenous variables, forecasted values of
these exogenous variables are prerequisites to forecast the endogenous variable.37 The
same is true for VAR and VEC models. These models combine the characteristics of
time series and multivariate regression models. Most of the literature assigns them
superior forecasting results in the short and in the long run.38 The validity of this fact
was however recently questioned for the real estate market by Gallin (2006) as well as
Wheaton & Nechayev (2008).
The statements of this subchapter are summarized in table 1. This overview
depicts the different natures of the examined models. Each model thus is applicable for
real estate market forecasting. However, according to theory it depends on the
circumstances under which model performs best, for instance, GARCH in volatile
markets, ARIMA for short-run forecasts, etc. Furthermore, the application of the
36
This is represented in McNees (1982) in more detail.
37
This fact is discussed in more detail in the next subchapter.
38
For real estate evidence refer to Stevenson & McGarth (2003).
32
models depends on the data availability. Since real estate markets are illiquid and
heterogeneous, data availability and also data quality are very limited for many
markets. According to few observations accompanied by the high aggregation of the
annual data for many German office markets, I cannot apply VAR or VEC models in
the empirical part of this work. An examination and a verification of the theory cannot
be executed at the moment. For the same reason, GARCH and ARIMA model
forecasts can furthermore only be tested for the rent series.
Table 1: Model overview
Regression
ARIMA
GARCH
VAR
VECM
Applicable with time series data
yes
yes
yes
yes
yes
Applicable with panel data
yes
no
no
yes
yes
Minimum of data observations
30
30
30+X
30+X
30+X
Consideration of cyclical motions
yes
yes
yes
yes
yes
Consideration of exogenous variables
yes
no
no
(yes)
(yes)
Consideration of economic theory
yes
no
no
no
yes
Consideration of autocorrelation
(yes)
yes
yes
yes
yes
Consideration of volatility cluster
no
no
yes
no
no
Short forecasting period preference
no
yes
yes
yes
yes
Long forecasting period preference
yes
no
no
yes
yes
3.4. Forecasting techniques and forecasting performance measures
Since in the empirical part of this work I apply dynamic one step out-of sample and
multistep out-of sample forecasting, I briefly explain these techniques in the
subsequent subchapter. In this context I discuss conditional and unconditional
forecasts. In the second part of this chapter, I talk about forecasting performance and
therefore I present and explicate two widely accepted performance measures.
33
3.4.1. Forecasting techniques39
To forecast a time series one needs a forecasting model. Different models have been
presented and evaluated throughout the last subchapter. Within the empirical part of
this work, I will apply some of these models to forecast office rent and office total
yield time series. In forecasting, different opportunities appear and have to be
distinguished. Besides others
x one-step-ahead forecasting vs. multistep-ahead forecasting
x in-sample forecasting vs. out-of sample forecasting
x static forecasting vs. dynamic forecasting
x conditional forecast vs. unconditional forecast
are important criteria to decide on.
In the subsequent chapters I execute one-step-ahead forecasts and multistepahead forecasts up to nine years. These forecasts are based on dynamic out-of sample
forecasting. The expression out-of sample implies that the forecasting period starts
after the last period included in the data sample which was applied to estimate the
forecasting model. In contrast, in-sample forecasting predicts values for a period
whose data is included in the underlying model estimation. Dynamic forecasting
requires dynamic elements, thus, either an underlying model with lagged dependent
variables or ARMA terms, as also implied in the autocorrelation correction undertaken
in the empirical part of the work at hand. Thus, before that step, forecasted values for
the lagged dependent variables are employed to forecast the current value. In static
forecasting actual values of the lagged dependent variables are used. Consequently,
dynamic forecasting is more susceptible to large forecast errors, the longer the
forecasting horizon becomes.
An unconditional forecast is one in which the independent variables have to be
forecasted themselves before they are implemented into the model to explain and
forecast the dependent variable. In contrast, in conditional forecasting assumptions for
the values of the independent variables are made. This approach serves to examine
different scenarios; hence, conditional forecasting is simply another term for scenario
analysis. For the empirical part of this work unconditional forecasts are applied in the
univariate analysis. Since in general the exogenous variables in the multivariate setting
39
Diebold (2001), Hanke & Wichern (2009), or Wilson (2007) give good overview of the topic of
forecasting.
34
are not determined for future periods either, they also have to be forecasted upfront.
This is a further source for increased forecasting errors of the endogenous variable
forecasts. In this work, however, I chose test forecasting periods for the models from
the past, from the late 1990s until 2006. This was mainly done to use actual values of
the forecasting periods to check the performance of the dynamic multistep out-of
sample forecasting models. As a secondary effect, no exogenous variables had to be
forecasted, which helped to avoid forecasting errors.
3.4.2. Forecasting performance measures
The first question after the forecasts have been made deals with their accurateness and
performance. An answer to this question is important for determining whether the
forecast is reasonable in general and thus whether the underlying model is well
specified. Additionally, the respective evidence is interesting when comparing
different forecasting results that depend on different underlying models.
In the literature one can find numerous measures that are able to illustrate the
performance of a certain forecast.40 One that is widely applied is the Root Mean
Square Error (RMSE).
T s
Measure 1:
¦ ( yˆ
t
yt ) 2 / s
t T 1
Measure 1 depicts the RMSE, with yˆt as the forecasted value of y the endogenous
variable and thus yˆt y as the forecast error. The sum of the squared forecast errors is
divided by s, the number of forecast values, to get an average value. From this result
the square root is extracted, which implies that RMSE give great weight to larger
errors. Furthermore, the canceling of positive and negative errors is avoided. In
general, one can say that the smaller the outcome of the measure, the better the
forecasting ability of the underlying model is. However, it is measured in the original
unit.
Another well-known forecasting performance measure is the Mean Absolute
Percentage Error (MAPE).
T s
Measure 2: 100 ¦
t T 1
40
yˆt yt
/s
yt
An overview of performance measures is delivered for instance in Kirchgässner (2007, p. 84 ff.),
Wooldridge (2009, p. 651 f.), Diebold (2001, p. 287 ff.).
35
Measure 2 depicts the MAPE, with yˆt as the forecasted value of y the
endogenous variable and thus yˆt y as the forecast error. In contrast to the RMSE,
here, the forecasted error is divided by y, representing a relative measure which does
not depend on the scale of the endogenous variable. Thus, forecasting performances
depending on different underlying series and models become comparable. In this case,
the canceling of the sum of positive and negative errors is avoided by taking absolute
values of the percentage expressions. The average percentage forecast error is finally
received by dividing by s, the number of forecast values, and multiplying by 100.
36
4.
Design of the empirical study
According to the classification in the literature review and the chapter on the
theoretical foundations, there are three major groups of forecasting models to achieve
rent, price, and total yield forecasts. On the one hand, there are univariate forecasting
models, whose forecasts are generated by applying only lagged values of the
dependent variable. On the other hand, there are multivariate regression models
introducing explanatory variables to forecast the dependent variable. Furthermore,
there are VAR and VEC models which combine both methods in order to explain the
dependent variable through lagged dependent variables as well as the lags of other
explanatory variables.
Seeking to apply and test the univariate as well as the multivariate regression
forecasting models and interpret their forecasts for the German office market, I carry
out an exclusive empirical study in the two subsequent chapters. In chapter 5, I thus
focus on the rent series as the examined endogenous variable. In chapter 6 the
investigation is undertaken for the total yield, a measure considering price changes
additional to rent changes.
The chapter at hand therefore introduces the design of this empirical study. In the
first subchapter I present the research hypotheses based on the research questions. The
next subchapter explains the research methodology. Finally, the adopted data is
illustrated.
4.1. Research hypotheses
Chapters 5 and 6 comprise the empirical section of this work. I will deliver explicit
answers to the research questions in chapter 1. Based on research questions 2 to 4 and
their accompanying sub-questions, I now develop 16 research hypotheses. Hypotheses
1 to 10, which cover office rent forecasting issues, are tested in chapter 5. Chapter 6
deals with the empirical testing of hypotheses 11 to 16, which examine office total
yield forecasting concerns. Total Yield hypotheses 11 to 16 are similar to several of
the rent hypotheses 1 to 10 in order to establish comparability. Nevertheless, a
completely identical investigation regarding forecasting models is not possible, since
the total yield data series is too short. Consequently, the univariate analysis cannot be
conducted, and hence, some of the hypotheses examined for the rent models are not
testable for total yield data.
37
x Research Hypothesis 1: Univariate as well as multivariate regression models
are not appropriate to forecast rent series in the German office market.
x Research Hypothesis 2: GARCH models do not help to outperform simple
ARIMA models in times of increased volatility.
x Research Hypothesis 3: There are no economic or real estate variables that
significantly influence the development of the rent series.
x Research Hypothesis 4: To construct a multivariate model which convincingly
performs in forecasting the rent series, a single demand and a single supply
proxy are not sufficient.
x Research Hypothesis 5: There are no cities where one model is permanently
superior regarding forecasting performance.
x Research Hypothesis 6: Univariate models do not result in superior forecasts
for rent series in major German cities, especially in the short run.
x Research Hypothesis 7: A multivariate single equation model with economic
explanatory variables does not produce superior forecasts, especially in the long
run.
x Research Hypothesis 8: The long-run rent level is not mainly determined by its
economic fundamentals.
x Research Hypothesis 9: Speculative factors play a role in the long-run
determination of the rent level.
x Research Hypothesis 10: A forecast starting value at a point in time when rents
are at an economically reasonable level is not crucial to precisely predicting the
rent level in the longer run.
x Research Hypothesis 11: Multivariate regression models are not appropriate for
forecasting total yield series in the German office market.
x Research Hypothesis 12: There are no economic or real estate variables that
significantly influence the development of the total yield series.
x Research Hypothesis 13: To construct a multivariate regression model which
performs convincingly in forecasting the total yield series, a single demand and
a single supply proxy are not sufficient.
x Research Hypothesis 14: The long-run total yield level is not mainly
determined by its economic fundamentals.
38
x Research Hypothesis 15: Speculative factors play a role in the long run
determination of the total yield level.
x Research Hypothesis 16: A forecast starting value at a point in time where total
yields are at an economically reasonable level is not crucial to precisely
predicting the total yield level in the longer run.
4.2. Research methodology
In chapters 5 and 6, the empirical section of this work, I test these 16 research
hypotheses step by step. Research hypotheses 1 to 10 are treated in chapter 5. I
therefore firstly construct and estimate city-specific ARIMA models and generate outof sample forecasts for the one-year up to the five-year forecasting horizon
afterward.41 In order to do this, I start with stationarity tests for the respective city
series, which I accomplish by applying the Phillips-Perron test. Afterward all nonstationary city series are first differenced. Again, the series are tested for stationarity.
Because some Phillips-Perron test results do not generate clear outcomes, the
Augmented Dickey-Fuller test is applied additionally for all series. In case the first
differenced series are non-stationary again according to their test results, they are
differenced once more. The Phillips-Perron and the Augmented Dickey-Fuller tests are
conducted once more.42 Subsequently, I employ correlograms of the stationary series
to identify possible ARMA structures.43 Then, these possible structures are estimated
and dynamic out-of sample forecasts are conducted. This is done for all different
forecasting horizons by adjusting the sample size.44 Afterward, performance measures
are calculated to determine the best performing ARIMA processes for out-of sample
forecasting. The measures applied are RMSE and MAPE. Each city’s ARIMA
41
This is not conducted for the rent series of Leipzig, since this series consists of considerably less
than 30 observations. And this turns out to be too short to be represented as an ARIMA process. This
point is discussed in detail in chapter 3.3.
42
Test results are illustrated in the appendix. For the level tests I added a constant and a trend. For the
first and second difference tests, I removed the exogenous trend variable, because of the detrended
series. Automatic eviews lag length criteria were implemented. The series of the reduced sub-samples
brought very similar results. The results are not reported; however, they are available upon request.
43
The different correlograms are not depicted here, but are available upon request. Since according to
chapter 4.3 all applied data is annually recorded, no seasonality estimations are executed.
44
For instance, a two-year out-of sample forecast is conducted by excluding the observations of the
years 2005 and 2006. Thus, the forecasting model is estimated with a sample which only includes
observations until 2004. Forecasts are then conducted for 2005 and 2006. This approach is chosen to
compare the forecasts with the values actually recorded in 2005 and 2006 and thus to determine the
best performing model.
39
investigation is completed by showing and interpreting the actual forecasts of the best
fitting model specifications for one up to five years.
In a next step, two cities’45 ARIMA process performances are improved by
applying GARCH forecasting models.46 This approach is chosen, since both cities
demonstrate a high upswing followed by a steep downturn in rent levels leading to
increased volatility in the period examined.47 Since the same rent series are applied as
for the simple ARIMA specifications, the test results regarding stationarity do not
change. Hence, the basis for the forecasts stays the same. Adopting the ARIMA
specifications for both cities for the first equation of the GARCH(p,q) model that
proved to be best fits in the single ARIMA model, I estimate possible ARIMAGARCH model structures by varying the GARCH variance configuration. I
furthermore conduct dynamic out-of sample forecasts. Again, the performance
measures RMSE and MAPE are calculated to determine the best performing
ARIMA(p,d,q)GARCH(p,q) processes for out-of sample forecasting. Both cities’
ARIMA(p,d,q)GARCH(p,q) investigation is completed by showing and interpreting
the actual forecasts of the best fitting model specification for one up to five years.
Additionally, the results are compared to the outcomes of the simple ARIMA
forecasting models.
Subsequently, economic and office real estate market indicators are tested for
their influence on the office rent series. For this analysis I apply panel data subsuming
the nine major German city office markets chosen. Using panel data offers many more
observations and thus better conditions for estimating the general underlying relations
of the endogenous with the exogenous variables.48 Therefore, I run panel unit root tests
for the combined city series and general unit root tests for series covering the total
German market.49 When non-stationary results are generated, series are first
45
The cities are Frankfurt and Munich.
46
This approach is chosen according to the approach applied by Crawford & Fratantoni (2003), who
pioneered this model in the real estate market.
47
Both cities' rent levels skyrocketed and crashed due to the cities' economic focuses on New
Economy and Financial companies. This period is known as the "Internet Bubble" or "New Economy
Bubble".
48
A single city analysis based only on the city-specific time series would have led to non-efficient
estimates due to the very short time series. On the other hand, the application of first differences with
panel data eliminates the influences of city-specific unobserved effects, thus coping with the real estate
market-inherent heterogeneity.
49
To test for stationarity I executed the Phillips-Perron test as well as the Hadri-Z-stat for panel data.
The tests for the national data are the same as for the long-run rent series. In both approaches I added a
constant and a trend for the level tests. For the first and second difference tests I removed the
exogenous trend variable because of the detrended series. Automatic eviews lag length criteria were
40
differenced and tested for stationarity once more. For series stationary at the second
difference, panel cointegration tests are executed to test for an implementation of error
correction models.
Afterward, I conduct a correlation analysis between the first differenced rent
series and those indicators in stationary form. Indicators showing influence on rent
series are then applied to construct multivariate forecasting models for the one-year up
to the five-year forecasting horizon. First, I implement the first differences of single
demand and supply proxies, which turned out to have significant influence on the rent
level change in the model.50 In doing so, I am following the logic that a price is
determined by demand as well as supply factors in a free market. After setting up this
basic equation, I analyze all possible combinations with the other variables regarded as
influential according to the correlation examinations in order to come up with a more
complex and possibly significant model. Furthermore, the model's estimation is
corrected regarding first order autocorrelation by applying the procedure developed by
Cochrane & Orcutt (1949).51 The different models are compared regarding their
performance measures. Subsequently, for the best performing models, dynamic out-of
sample forecasts are conducted and interpreted for the one-year up to the five-year
forecasting horizon. There, the actual values of the exogenous variables are
implemented for the forecasts in order to come up with general evidence of the
model’s performance.52
In a next step, these forecasts are compared to those of the univariate models
using graphs, forecasted figures as well as performance measures. The patterns
detected are analyzed and interpreted.
Finally, multivariate models are estimated to execute long-run rent forecasts.
Therefore, the same estimation equation is applied as for the one-year to five-year
models; however, the estimation sample is adjusted. This means that, depending on the
respective city, longer out-of sample forecasting horizons are generated, which is
meaningful in analyzing the appropriateness and precision of the models in the long
implemented. All test results are illustrated in the appendix. The series of the different sub-samples
produced very similar results. The results are not reported; however, they are available upon request.
50
This basic approach is chosen according to the approach applied by Gardiner & Henneberry (1988).
51
This approach was also chosen by Wheaton & Nechayev (2008) for their single equation model.
52
VAR and VEC are not applied since a meaningful forecasting equation could not be established.
Due to the high degree of aggregation of annual data as well as the low availability of observations,
the executed lag structure could not represent the causal relations adequately. In any case, according to
Gallin (2006) and Wheaton & Nechayev (2008), the appropriateness and superiority of such models
applied in the real estate market is questioned.
41
run. The sample size and thus the starting value for the forecasts are chosen with
respect to the best performance measures. Finally, the outcomes are analyzed and
interpreted.
In chapter 6 the hypotheses concerning total yield forecasting models are
examined. As already clarified, the univariate analysis is not possible. Thus, I only
conduct the multivariate regression examination. The procedure for stationarity
testing, correlation analysis, model construction, as well as short- and long-run
forecasting is the same as for the rent series.
4.3. Data
In this subchapter I present the definition and the source of all applied time series.
Rent and total yield series of each office real estate market under study as well as
variables having assumable influence on the rent series are considered.
The nine individually investigated German office markets are:
x Cologne
x Dusseldorf
x Essen
x Frankfurt
x Hamburg
x Leipzig
x Munich
x Nuremberg
x Stuttgart
These cities were chosen, because they represent most of the major German
office markets. All of these markets have some important characteristics in common.
For all cities sufficient data regarding rent and total yield series as well as potentially
42
explanatory variables is available.53 The data has good quality. This is guaranteed by
many active brokers and consultants in the specific markets. Furthermore, even though
the chosen markets are very heterogeneous with many additional individual
characteristics, the combined view of the cities provides at least a general picture of
the total German office market and especially its rent and total yield development.
4.3.1. Rent series
All individual rent series are taken from the Feri Real Estate Database. The primary
sources are the Statistisches Bundesamt, the Statistische Landesämter , the Ring
deutscher Makler e.V., the Verband deutscher Makler e.V, as well as
Gutachterausschuesse der Kommunen.
The analyzed rent series are defined as offices situated in secondary locations.
The further definition is "Rent per month (ex heating expenses and additional costs)
for the commercial use of office space of average utility value (mean value across
rents for simple utility value (e.g., commercial area, built before 1950, nonrepresentative location), office space of good utility value (e.g., normal equipped new
buildings with average traffic junctions) in suburban location (Euro/m²). The numbers
come from different sources and are checked and transformed by Feri Rating &
Research GmbH."54
Moreover, the rent data is nominal and annually recorded; it is collected on an
average basis from the 1st of January until the 31st of December of the respective
year.55 Most cities' series start in the 1970s.
4.3.2. Total Yield series
All individual total yield series are taken from the Feri Real Estate Database. The
primary sources are the Statistisches Bundesamt, the Statistische Landesämter, the
Ring deutscher Makler e.V., the Verband deutscher Makler e.V., as well as
Gutachterausschuesse der Kommunen.
The exact definition of the total yield is:
53
The only exception is Leipzig, where the rent series consists of considerably less than 30
observations. This turned out to be too short to be represented as an ARIMA process, a point which is
discussed in detail in chapter 3.3.
54
Feri Rating & Research GmbH (2007), page 21.
55
Confirmed by Manfred Binsfeld, Feri Rating & Research GmbH
43
Definition 1: Total Yield = Rental Yield + Price Yield
The definition of the rental yield is:
Definition 2: Rental Yield =
annualized rentt
pricet 1
The definition of the price yield is
Definition 3: Price Yield =
pricet pricet 1
pricet 1
These definitions make clear that the total yield series is expressed in relative
terms, which is different compared to the underlying rent and price series, which are
represented in absolute terms. For a more detailed definition regarding the rent series
please refer to chapter 4.3.1.56 The price series is mainly calculated on the basis of the
respective rent data. The exact composition is not published by Feri Rating &
Research GmbH. Since the price series is only collected from 1992 on the total yield,
the series does not start before 1993.
4.3.3. Potentially explanatory variables
Depending on general real estate and economic theory and the real estate forecasting
literature outlined in chapters 2 and 3, several potential explanatory variables were
chosen for the empirical investigation of this work.
The following potential explanatory variables under study are also taken from the
Feri Real Estate Database:57
56
57
Also check at Feri Rating & Research GmbH (2007), page 21.
The primary sources are Bundesagentur fuer Arbeit, Statistisches Bundesamt, Statistische
Landesämter,
Arbeitskreis
volkswirtschaftliche
Gesamtrechnung,
and
Arbeitskreis
44
x Office Employees
x Office Space Inventory
x Vacancy; Office Space
x Gross Value Added; Public & Private Services
x Gross Value Added; Financial & Other Services
These series are indicators directly taken from the broader real estate markets.
All series start in 1992 and are city-specific annual data. They are collected on an
average basis from the 1st of January until the 31st of December of the respective year.
The only exception is the series "Office Employees", where the depicted value is the
number of office employees on the 30th of June of the respective year. Furthermore,
the "Gross value added" series are given in real terms with basis 2000. This individual
city data is combined in the subsequent examination and forms a panel data set.
Moreover, I analyze the following series, which are taken from Thomson
Datastream:58
x Consumer Price Index, Germany
x Construction Price Index-new office buildings, Germany
x Germany Interbank 12 mth (LDN: BBA) - offered rate
x Germany (DEM) IR Swap 10 Year - middle rate
All of these series are collected for Germany, and thus, it is not city-specific data.
Since the literature indicates that rents are not only influenced by localized economic
data, national economic data is also considered. Furthermore, the series are
transformed into annualized data.
Erwerbstätigenrechnung for socio-economic parameters and construction activity. The primary
sources for real estate market indicators are the same as mentioned for the rent series in chapter 4.3.1.
58
http://www.datastream.com/
45
5.
Empirical results: Rent forecasting
This chapter presents the empirical results on rent forecasts in the German office
market. Therefore, I examine the general appropriateness and performance of the
different models for the above-mentioned nine cities in the one to five-year period.
The examination is conducted for the univariate ARIMA and GARCH models in
subchapter 5.1 as well as for the multivariate regression model in subchapter 5.2.
Furthermore, in subchapter 5.3, the results are compared and interpreted and thus used
to detect individual characteristics of the cities. Additionally, in subchapter 5.4, an
investigation on long-run models is conducted. The chapter concludes with subchapter
5.5.
5.1. Univariate models
Chapter 5.1 is subdivided into subchapter 5.1.1, which presents a rent data series
analysis. Subchapter 5.1.2 illustrates the construction, estimation, and the forecasts of
ARIMA models for each city. In subchapter 5.1.3, GARCH models are applied for two
cities, while the differences between and interesting patterns of these two
specifications are discussed in 5.1.4.
5.1.1. Rent data analysis
In this subchapter I examine each individual city's rent series graphically. The detailed
interpretations I provide are evaluated at the end of the paragraph. Finally, I apply unit
root tests to study each series regarding stationarity.
x Cologne:
The Cologne rent series starts in 1972. This series can be subdivided into three major
phases. Until the mid 1980s, the series can be described as relatively steady, showing
little volatility except for a minor peak in 1981. From the late 1980s until the early
1990s, a tremendous increase can be observed. Due to the economic boom and
German reunification, the rent level more than triples in this period. Afterward, graph
2 again exhibits a steady development, however, this time with a decreasing tendency
that is interrupted only by an interim peak around the year 2000. The results of the
Phillips-Perron unit root test for this series clearly underline non-stationarity, as can be
seen in tables 1 and 2 in the appendix.
46
Graph 2: Cologne Rent Series
11
10
9
8
7
6
5
4
3
2
1970
1975
1980
1985
1990
1995
2000
2005
Cologne
Consequently, the series is transformed into its first differences. The results of
the Phillips-Perron test as well as the Augmented Dickey-Fuller test show that the
hypothesis of a unit root can be rejected on the 5% level and that the first differenced
series is stationary.
x Dusseldorf:
Graph 3: Dusseldorf Rent Series
14
12
10
8
6
4
2
1970
1975
1980
1985
1990
1995
2000
2005
Dusseldorf
In Dusseldorf the rent level steadily increases until 2002, with an accelerated
phase between the late 1980s and the early 1990s. After 2002 there is a dramatic drop
which does not end until 2005. While the economic boom and German reunification
can again be considered as reasons for the increased upswing, the rent crash after 2002
can only be explained by a massive jump in office space supply after 2004. This was
47
apparently anticipated by market participants well in advance so that rents as well as
prices did react early.59 The Dusseldorf rent series in levels is non-stationary.
However, the first differences of the series are stationary on the 5% level with respect
to both tests. This can be observed in tables 1 and 2 in the appendix.
x Essen:
Graph 4: Essen Rent Series
7.0
6.5
6.0
5.5
5.0
4.5
4.0
3.5
3.0
1970
1975
1980
1985
1990
1995
2000
2005
ESSEN
The Essen rent series starts in 1972. Again, I detect three major phases over the
last three decades. Similarly to Cologne, the series presents a steady development until
the mid-1980s. Furthermore, there is a clear rent level upswing in the period of the
economic boom and German reunification, during which time t rents almost double.
Afterward, graph 4 again exhibits a steady development, with a decreasing tendency.
With the Essen rent series, I detected a special case. Here, the level series and also the
first differenced series is non-stationary.60 Only the series which is differenced twice is
stationary on the 5% level with respect to both tests, as can be observed in tables 1, 2
and 3 in the appendix.
59
Figures regarding office space inventory change for Dusseldorf in the years mentioned are not
depicted here. However, they can be provided by the author upon request
60
On the one hand, the Phillips-Perron test's output shows stationarity in the first differenced series.
On the other hand, the Augmented Dickey-Fuller test contradicts that. After taking into consideration
the performance measures, I decided to difference the Essen rent series one more time.
48
x Frankfurt:
Graph 5: Frankfurt Rent Series
20
16
12
8
4
0
1970
1975
1980
1985
1990
1995
2000
2005
Frankfurt
For the Frankfurt rent level I note five different phases. Until the mid 1980s the
series describes a steady development, as illustrated in graph 5. Then, in the late 1980s
until the early 1990s, one can detect a remarkable upswing due to the economic boom
and German reunification. In the next period until the late 1990s there is again a time
where rents are moving to the side. From the late 1990s until 2001 there is a further
rise in the rent level to a peak of 19.3 € per m² and month. In the last phase, the final
upswing is followed by a significant drop, which bottoms out at 12.5 € per m² and
month. The second major upswing and the downturn afterward happen in the time of
boom and bust of the New Economy, in which very high stock market prices allowed
many start-ups to pay very high rents for their new office space. Furthermore, referring
to tables 1 and 2 in the appendix, the Frankfurt rent series in levels is non-stationary.
Nevertheless, the first differences of the series are stationary on the 5% level with
respect to the Pillips-Perron and also the Augmented Dickey-Fuller test.
x Hamburg:
The Hamburg rent series can be subdivided into five phases. Until the late 1980s
the series increases significantly: Starting in 1977, the level almost doubles. However,
after 1989, there is a steep and rapid increase. The peak following the German
reunification boom in 1992 is almost at 10 € per m² and month. The upswing gives
way to a decline between 1992 and 1998.
49
Graph 6: Hamburg Rent Series
10
9
8
7
6
5
4
3
1970
1975
1980
1985
1990
1995
2000
2005
Hamburg
From 1998 until 2001, another rise in the rent level can be observed in the course
of the New Economy boom. Nevertheless, this increase does not reach the all time
high of 1992. Instead, rents subsequently fall to the levels of the 1980s. Moreover, the
Hamburg level rent series is non-stationary. Although the first differenced series tests
for stationarity show contradicting results, I continue to work with the first differenced
series after taking into consideration the performance measures of tested ARIMA
forecasting models using the once and also the twice differenced rent series.61
x Leipzig:
Graph 7: Leipzig Rent Series
14
12
10
8
6
4
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Leipzig
61
On the one hand, the Phillips-Perron test's output misses the 5% as well as the 10% confidence level
and thus does not tend to stationarity in the first differenced series. On the other hand, the Augmented
Dickey-Fuller test clearly contradicts this and provides strong evidence for a stationary process in the
first difference. Please refer to tables 1 and 2 in the appendix.
50
The Leipzig rent series clearly manifests its own pattern in comparison to the
other cities. This can be observed in graph 7. Since Leipzig is situated in the Eastern
part of Germany, the free market rent series is only available for the years after 1992.
The Leipzig rent series can be subdivided into two major phases. The first period is the
time of a tremendous drop in rent level after 1992. With its initial point being a peak in
the aftermath of German reunification, including a huge speculative portion within the
rent, this significant decline ends around 1997. Afterward, the rent level development
is relatively stable, however, with a further decreasing tendency. Due to the short rent
series, I could not perform a unit root test for Leipzig. However, Leipzig is included in
the multivariate investigation and thus in the combined city rent series. This shows
non-stationarity in the levels but is stationary when first differenced, as the panel unit
root tests in tables 6 and 7 of the appendix illustrate.
x Munich:
Graph 8: Munich Rent Series
13
12
11
10
9
8
7
6
5
4
1970
1975
1980
1985
1990
1995
2000
2005
Munich
The Munich rent level appears more volatile than other cities. I observe five
different phases. Until the mid 1980s, the series describes a steadily increasing rent
level path. After 1985 there is a remarkable upswing until 1992 due to the economic
boom and German reunification. After this interim peak and until 1997, the rent level
massively drops by almost one-third. From 1998 until 2001 there is again an extreme
upswing in the rent series. Nevertheless, after this all time peak of 12.5 € per m² and
month, an even more dramatic decline can be observed. Boom and bust around the
millennium can be attributed to the rise and fall of the New Economy. As I discovered
for the Essen rent series, the Munich rent series also has to be differenced twice to
51
become stationary. Both tests clearly demonstrate non-stationarity for the level and
also the first differenced series. However, both test results clearly show stationarity for
the second differences.62
x Nuremberg:
The Nuremberg rent series can be subdivided into four major phases. Until the
mid 1980s the series presents a steady development. From the late 1980s until the
early 1990s, a tremendous increase can be noticed. The rent level almost doubles
during the economic boom and German reunification. In graph 9 one can observe a fall
in rent level from 1992 until the mid-1990s followed by a steady development, which
is interrupted only by an interim peak around the year 2000.
Graph 9: Nuremberg Rent Series
8
7
6
5
4
3
1970
1975
1980
1985
1990
1995
2000
2005
Nuremberg
The level rent series of Nuremberg is non-stationary. Testing the first differenced
series for stationarity according to the methodology of Phillips-Perron, the test
displays an outcome which only marginally rejects the hypothesis of stationarity.
However, the Augmented Dickey-Fuller test results demonstrate stationarity at the 5%
level, as can be observed in tables 1 and 2 in the appendix. Thus, in the course of this
study, I apply the Nuremberg first differenced series.
62
Please refer to tables 1, 2 and 3 in the appendix.
52
x Stuttgart:
For the Stuttgart rent series I detected four major phases. Until the late 1980s the
series presents a steady development with a slight average increase. From the late
1980s until the early 1990s, a tremendous increase can be seen which reaches its peak
in 1993. The rent level almost doubles in this period of economic boom and German
Reunification. After 1993 the rent level decreases until the late 1990s followed by a
steady development that is interrupted only by an interim peak around the year 2002.
Compared to similar patterns of other cities' series, the Stuttgart rent series follows the
path one to two years later.
Graph 10: Stuttgart Rent Series
11
10
9
8
7
6
5
4
3
1970
1975
1980
1985
1990
1995
2000
2005
Stuttgart
For Stuttgart, on the one hand, the level rent series is also non-stationary, either.
On the other hand, the first differences of the series are stationary at the 10% and at the
1% level with respect to the Phillips-Perron or the Augmented Dickey-Fuller test.63
According to this city analysis, I detect a general rent pattern for Cologne,
Dusseldorf, Frankfurt, Hamburg, Munich, Nuremberg, and Stuttgart. All of these cities
have peaks around the years 1992 and 2001, with an intermediate trough in between.64
Essen and Leipzig show a rent pattern different from the other cities. They seem to be
somehow independent from the other rent markets. Essen, on the one hand, shows the
peak in the early 1990s. However, instead of a second peak around 2001, the Essen
rent series declines after 1996 on average. The special development of
63
64
Refer to tables 1 and 2 in the appendix.
Besides this similar pattern one has to be aware of the fact that both the level and the exact shape of
the amplitude are different throughout the cities.
53
Essen’s office market can be explained by the high degree of transformation from
heavy industries to service industries which the city, as a part of the Ruhr Area, had to
undergo. On the other hand, the Leipzig rent series is very short and was only
collected after 1991. Since Leipzig is situated in the eastern, former communist, part of
Germany, no data is available for the years before German reunification. The
beginning of the presented period witnessed an enormous amount of speculation, and
in the aftermath of the reunification, there was great industry transformation as well as
societal change. Thus, the special behavior of the rent series, which manifests its peak
in 1992, can be explained to a great extent by such historical developments.
Remarkable is, that instead of a second peak around 2001, the rent series steadily
declines from 1992 until present.
Concluding, with respect to rent series, most of the major German office markets
analyzed demonstrate a similar pattern, which hints at a broad rent market with high
interrelations between these cities. Only two cities are considered explainable
exceptions.
5.1.2. ARIMA models: Construction, estimation, and forecasting
Within this subchapter there is a general procedure to arrive at the best fitting ARIMA
forecasts for each city. At first, I identify and estimate possible ARMA structures for
the stationary city rent series. Dynamic out-of sample forecasts are conducted and
performance measures are applied to determine the best performing ARIMA processes
for out-of sample forecasting. Each city’s ARIMA investigation is completed by
showing and interpreting the actual forecasts of the best fitting model specification for
one up to five years.
x Cologne:
According to the investigation in subchapter 5.1.1 and tables 1 and 2 in the
appendix, the hypothesis of a unit root is not rejected for the Cologne rent series in
levels. Stationarity however is accomplished for the first differenced series. Applying
this series, an ARIMA(4,1,0) process is detected as the best fitting ARIMA model for
Cologne, independent of the sample time frame. The performance measures of the
ARIMA(4,1,0) specifications are shown in table 10 in the appendix. Furthermore, the
outcomes indicate good forecasts for the one- to three-year models. On the other hand,
54
they illustrate more imprecise forecasts for the two longer periods. The coefficient
estimations prove to be very stable, with a positive sign for the coefficients of the
AR(1) and the AR(3) terms and a negative sign for the AR(2) and the AR(4) terms
respectively, whereas only the coefficients of AR(1) and the AR(4) prove to be
significantly different from zero. These results are depicted in table 11 in the appendix.
Table 2: ARIMA Rent Model Forecast Outcomes – Cologne
Cologne
Actual series
1998
1999
2000
2001
2002
2003
2004
2005
2006
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.8
7.5
One-year
Two-year
ARIMA(4,1,0) ARIMA(4,1,0)
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.8
7.7
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.9
7.8
Three-year
Four-year
Five-year
ARIMA(4,1,0)
ARIMA(4,1,0)
ARIMA(4,1,0)
8.4
8.7
9.1
9.4
9.1
8.4
7.9
7.5
7.4
8.4
8.7
9.1
9.4
9.1
8.8
8.6
8.4
8.3
8.4
8.7
9.1
9.4
9.5
9.6
9.5
9.3
9.2
The one-year forecast for the Cologne rent series provides a prediction that
correctly anticipates the continued downward development in 2006, while the level is
a bit overestimated, as illustrated in table 2. The two year forecasts also show the right
direction; again, however, a slight overestimation can be discerned. Besides a slight
exaggeration in the downturn in the years 2004 and 2005, the three-year forecasting
model presents a very precise level estimation for the year 2006. The four year
forecasting model does not show accurate level predictions. Although the direction is
correctly anticipated, the deviation of the forecasted to the actual value in 2006 is
already about 10%. An even greater deviation can be found for the five-year
forecasting model. A reason for this is that the extremum of the rent series in 2001,
when the boom was at its peak, is not anticipated correctly and is predicted for the year
2003. Thus, the rent series decline does not start before 2004.
The descriptions of the one- to three-year forecasts can also be tracked at graph
11, which also depicts the four- and the five-year forecasts. One can see that the
ARIMA forecasting model, with its starting point in 2002, the year directly following
the peak, shows poor level prediction as well as a late extremum.
55
Graph 11: ARIMA Rent Model Forecast Outcomes – Cologne
11.0
11.0
10.5
10.5
10.0
10.0
9.5
9.5
9.0
9.0
8.5
8.5
8.0
8.0
7.5
7.5
7.0
7.0
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Cologne
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Cologne
x Dusseldorf:
For the stationary first differenced Dusseldorf series, I apply an ARIMA(2,1,0)
process for all but one of the forecasting models. Based on the underlying performance
measures, the three-year forecasting model fits best when specified as an
ARIMA(2,1,2) model. As can also be observed at the different performance measures,
the forecasting power of the ARIMA model for the differenced Dusseldorf rent series
is very poor.65 Only the two-year forecast seems to be adequately accurate and
comparable with respect to its quality to the ARIMA forecasting results of other cities.
Except for the different specified three-year model, the coefficient estimations
demonstrate high stability, with a permanent positive sign for the AR(1) coefficient,
which proves to be significantly different from zero, and a permanent negative sign for
the AR(2) coefficient. However, this coefficient is never clearly significantly different
from zero. In the three-year model both AR(1) and AR(2) show negative coefficients,
whereas the MA terms have positive signs. They are depicted in table 13 in the
appendix. The two-year forecast demonstrates a good anticipation of the decrease in
rent level in 2005, even though it does not completely show the significant decline of
almost 15%.
65
This is illustrated in table 12 in the appendix.
56
Table 3: ARIMA Rent Model Forecast Outcomes – Dusseldorf
Dusseldorf
Actual series
1998
1999
2000
2001
2002
2003
2004
2005
2006
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.5
7.6
One-year
Two-year
ARIMA(2,1,0) ARIMA(2,1,0)
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.5
6.8
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.8
7.6
Three-year
Four-year
Five-year
ARIMA(2,1,2)
ARIMA(2,1,0)
ARIMA(2,1,0)
11.2
11.5
11.8
11.9
12.0
10.7
10.0
9.7
10.0
11.2
11.5
11.8
11.9
12.0
12.0
12.1
12.1
12.1
11.2
11.5
11.8
11.9
11.9
12.0
12.0
12.0
12.0
However, since the extremum in 2005 is not predicted in this model, again, the
level of the forecast for 2006 is very precisely anticipated. The three-year forecasting
model underestimates the drop in rent level by more than 30%. Nevertheless, the
extremum in 2005 is correctly predicted. The four- and the five-year forecasts both
show very poor forecasts. On the one hand, the extremum in 2005 once again is not
predicted. On the other hand, the extremum in 2002 is not anticipated either, leading to
a very strong overestimation of the rent level. The drop is not projected at all. Again,
the outcomes of the forecasts can also be observed when looking at graph 12.
Graph 12: ARIMA Rent Model Forecast Outcomes – Dusseldorf
13
13
12
12
11
11
10
10
9
9
8
8
7
6
7
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Dusseldorf
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Dusseldorf
57
x Essen:
For the Essen rent series I detected a special case, where the series is only
stationary when differenced twice.66 For Essen I apply an ARIMA(2,2,0) specification
for the one-, the three-, and the four-year forecasting models. For the two- and the
five-year forecasts, an ARIMA(3,2,0) model fits best.67 The coefficient estimations
always have the same direction. The AR(1) and the AR(2) coefficients show a
negative sign significantly different from zero; the AR(3) coefficients are always
positive when added. All coefficients are more or less in the same range, independent
of the forecasting model.
Table 4: ARIMA Rent Model Forecast Outcomes – Essen
Essen
Actual series
1998
1999
2000
2001
2002
2003
2004
2005
2006
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.3
5.3
One-year
Two-year
ARIMA(3,1,0) ARIMA(3,1,0)
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.3
5.3
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.2
5.1
Three-year
Four-year
Five-year
ARIMA(3,1,0)
ARIMA(3,1,0)
ARIMA(3,1,0)
5.8
6.1
5.9
5.6
5.5
5.5
5.4
5.3
5.2
5.8
6.1
5.9
5.6
5.5
5.4
5.2
5.1
4.9
5.8
6.1
5.9
5.6
5.7
5.6
5.3
5.3
5.2
The one-year out-of sample forecast is identical with the actual stable rent level
and can be considered a very precise result. The two-year forecast demonstrates a
weak underestimation of the actual level. Instead of predicting the actual steady
development, a weak annual decrease is estimated. The same pattern is valid for the
three-year forecast, where the drop in 2004 is correct, but slightly too weak regarding
the actual outcome. Also, because of this fact, the underestimation of the level until
2006 does not turn as strong as in the two-year forecast. This pattern also appears in
the four-year forecast. Here, the decrease is already anticipated in 2003, thus one year
too early leading again to a bigger level underestimation in 2006. However, this
underestimation is still less than 10%. The five-year out-of sample forecasting results
lead to a very precise level prediction throughout the last three years, showing exact
forecasts in 2004 and 2005 and only a slight underestimation in 2006. The first two
66
67
Please refer to Tables 1, 2 and 3 in the appendix.
The performance measures of the Essen's ARIMA specifications are shown in table 14 in the
appendix.
58
years however, show small overestimation, because for 2002 a non-existing extremum
is anticipated. These entire forecasting patterns can be observed when considering
graph 13.
Graph 13: ARIMA Rent Model Forecast Outcomes – Essen
6.6
6.8
6.4
6.4
6.2
6.0
6.0
5.8
5.6
5.6
5.4
5.2
5.2
4.8
5.0
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Essen
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Essen
x Frankfurt:
According to the output of the correlogram of the first differenced series as well
as by considering the performance measures for the tested ARIMA specifications I
apply an ARIMA(4,1,0) process for the Frankfurt one-year forecasting model and an
ARIMA(4,1,1) process for the two- to five-year forecasting models. By looking at the
average deviation of the four-year forecast of 21% and the five-year forecast of 40%
measured by the performance measure MAPE, the poor forecasting precision
regarding level estimation stands out.68 The AR(1) coefficient is positive within all
forecasting models, however, not significantly different from zero in the models
enriched with the MA(1) term. The coefficient of MA(1) is always significantly
positive and relatively stable around 0.8. The AR(2) and AR(3) coefficients are not
significantly different from zero independent of the forecasting model. However, the
AR(4) coefficient displays a positive sign significantly different from zero most of the
time, as can be seen in table 17 in the appendix.
68
This can be observed in table 16 in the appendix.
59
Table 5: ARIMA Rent Model Forecast Outcomes – Frankfurt
1998
1999
2000
2001
2002
2003
2004
2005
2006
Frankfurt
One-year
Actual series
ARIMA(4,1,0)
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.5
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.8
Two-year
ARIMA(4,1,1)
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.2
12.6
Three-year
ARIMA(4,1,1)
14.4
16.4
18.3
19.3
18.0
14.5
12.6
12.6
13.9
Four-year
ARIMA(4,1,1)
14.4
16.4
18.3
19.3
18.0
16.2
15.7
15.3
15.5
Five-year
ARIMA(4,1,1)
14.4
16.4
18.3
19.3
20.0
19.7
19.2
18.9
18.6
The one-year forecast predicted by an ARIMA(4,1,0) specification clearly
presents an overestimation of the actual level. Instead of the actual steady
development, the level is predicted approximately 2.5% too high. One could interpret
this, for instance, as a technical backlash regarding the tremendous drop in rent level
since 2001. According to table 5, the two-year forecast again offers a slight
overestimation in the final year. Since the forecasted value for 2005 underestimates the
actual level, the final overestimation is relatively moderate, even though one can
observe a similar upward movement in comparison with the one-year model. The
three-year forecasting model demonstrates a very precise level estimation for the first
two years, anticipating the rent drop in 2004 and the steady development in 2005 with
outstanding accuracy. However, the value of the last year is clearly overestimated by
more than 10%. As expected, by the performance measures the four- as well as the
five-year forecasts show a high deviation from the actual level. Within the four-year
outcomes, this results the underestimated rent drop in 2003 and 2004. For the five-year
forecasting model, more or less the same pattern is valid. In the end, the level is even
considerably higher, as in the four-year forecast, because the actual rent drop in 2002
is anticipated for 2003. At the same time, the forecast in 2002 still shows an upward
movement, as can be seen in graph 14.
60
Graph 14: ARIMA Rent Model Forecast Outcomes – Frankfurt
20
22
19
20
18
18
17
16
16
15
14
14
13
12
12
10
11
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Frankfurt
Three-year
Frankfurt
x Hamburg:
After first differencing the Hamburg rent series and considering the outcome of
the correlogram, I apply an ARIMA(2,1,0) specification for Hamburg, which is the
best fitting model for every year.69 The coefficient estimations always have the same
direction. The AR(1) coefficient always shows a positive sign and the AR(2)
coefficients always reproduce a negative sign. All coefficients are very much in the
same range and significantly different from zero, independent of the forecasting
model.
Table 6: ARIMA Rent Model Forecast Outcomes – Hamburg
Hamburg
Actual series
1998
1999
2000
2001
2002
2003
2004
2005
2006
69
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.8
6.8
One-year
Two-year
ARIMA(2,1,0) ARIMA(2,1,0)
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.8
7.1
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.6
6.7
Three-year
Four-year
Five-year
ARIMA(2,1,0)
ARIMA(2,1,0)
ARIMA(2,1,0)
7.4
7.7
8.2
8.5
8.1
7.2
6.6
6.5
6.7
7.4
7.7
8.2
8.5
8.1
7.7
7.4
7.4
7.4
7.4
7.7
8.2
8.5
8.6
8.6
8.6
8.5
8.5
The performance measures of the Hamburg’s ARIMA specifications are shown in table 18 in the
appendix.
61
The one-year forecast of the ARIMA(2,1,0) model shows a clear overestimation
of the actual level. Instead of a steady development, the level is predicted 4% too high.
The two-year forecast delivers a slight underestimation of the actual values in both
years. A reason for this seems to be that the trough in 2004 is anticipated for 2005. The
same pattern can be noticed in the outcomes of the three-year forecast model;
however, it starts with a very precise estimation of the rent drop in 2004 compared to
2003. The level in the four-year forecast model is overestimated. Since the drops in
2003 and in 2004 are correctly anticipated but predicted too low, the precision of the
last three years’ forecasts suffer. Finally, the five-year forecast model grossly
overestimates the actual rent development by about 25% in the last year. The
extremum in 2001 is not foreseen and thus, as can be seen in graph 15, the downward
direction of the rent is not depicted by the forecast outcomes.
Graph 15: ARIMA Rent Model Forecast Outcomes – Hamburg
10.0
10.0
9.6
9.5
9.2
9.0
8.8
8.4
8.5
8.0
8.0
7.6
7.5
7.2
7.0
6.8
6.5
6.4
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Hamburg
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Hamburg
x Munich:
For the twice differenced Munich rent series, I apply an ARIMA(2,2,2)
specification for the one-, the two-, and the five-year forecasting models. For the threeand the four-year forecasts, an ARIMA(1,2,2) model fits best.70 The performance
measures of the Munich one- to two-year forecasting models reveal very precise
forecasts. The coefficient estimations are very stable. They are significantly different
from zero. AR(1) is always positive. The MA terms show permanently negative signs,
70
The performance measures of the Munich's ARIMA specifications are shown in table 20 in the
appendix.
62
whereas the coefficient of MA(1) appears to be always significantly different from
zero. The same is true for the AR(2) term except in the five-year model.
Table 7: ARIMA Rent Model Forecast Outcomes – Munich
Munich
Actual series
1998
1999
2000
2001
2002
2003
2004
2005
2006
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.0
One-year
Two-year
ARIMA(2,2,2) ARIMA(2,2,2)
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.0
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.1
Three-year
Four-year
Five-year
ARIMA(1,2,2)
ARIMA(1,2,2)
ARIMA(2,2,2)
8.3
8.8
10.9
12.5
10.8
8.9
8.0
7.5
7.1
8.3
8.8
10.9
12.5
10.8
9.1
8.5
8.2
8.0
8.3
8.8
10.9
12.5
13.4
14.6
15.5
16.6
17.5
The one- and the two-year out-of sample forecasts provide very precise results. The
drops in rent level in 2005 and in 2006 are well predicted. The same is more or less
true for the three-year forecasting model, where there is only a weak overestimation
due to fact that the drop in 2004 is not completely anticipated. The four-year
forecasting model's output demonstrates a level that is clearly above the actual rent
because each year's drop is underestimated.
Graph 16: ARIMA Rent Model Forecast Outcomes – Munich
13
18
12
16
11
14
10
12
9
10
8
8
7
6
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Munich
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Munich
The five-year out-of sample forecast leads to a very imprecise level prediction, as
graph 16 also shows. The extremum in 2001 and thus the rent drop afterward are
63
completely missed by this model. Instead, the rent is predicted to increase further after
2001. The rent boom is expected to continue.
x Nuremberg:
For Nuremberg I work with the first differenced series and specify the best fitting
forecasting models as ARIMA(4,1,0) for the one- as well as the two-year models and
ARIMA(4,1,1) for the three- to five-year models. Worth mentioning are the
outstandingly low and thus very strong performance measures. As presented below
they are an indicator of very precise forecasts.71 The coefficient estimations for the two
ARIMA(4,1,0) are very much in line, showing significantly positive coefficients for
the AR(1) terms and negative ones for the AR(2), AR(3), and AR(4) terms. However,
only the AR(4) coefficient is significantly different from zero. For the ARIMA(4,1,1)
specifications, the AR(2), AR(4), and the MA(1) term show significant coefficients, a
positive for AR(2) and MA(1) and a negative for AR(4). The AR(1) and the AR(3)
terms are not significantly different from zero.
Table 8: ARIMA Rent Model Forecast Outcomes – Nuremberg
Nuremberg
Actual series
1998
1999
2000
2001
2002
2003
2004
2005
2006
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
6.0
One-year
Two-year
ARIMA(4,1,0) ARIMA(4,1,0)
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
6.1
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
6.1
Three-year
Four-year
Five-year
ARIMA(4,1,1)
ARIMA(4,1,1)
ARIMA(4,1,1)
5.8
6.0
6.4
6.3
5.8
5.7
5.5
5.6
5.9
5.8
6.0
6.4
6.3
5.8
5.6
5.3
5.4
5.7
5.8
6.0
6.4
6.3
6.0
5.8
5.6
5.8
6.1
The one- and the two-year out-of sample forecasts provides very precise results.
The slight increase in rent level in 2005 and the stronger one in 2006 are well
anticipated. Furthermore, regarding the two-year forecasting model, the extremum and
thus the trough in 2004 is anticipated correctly. The same is more or less true for the
three-year forecasting model, where there is only a weak underestimation. The results
of the four-year model also show an even bigger underestimation. However, compared
to other cities, an average deviation from the actual series of about 3.7% still indicates
71
The performance measures of the Nuremberg’s ARIMA specifications are shown in table 22 in the
appendix.
64
a very precise forecasting model. Even more impressive are the forecasts of the fiveyear model. With an average deviation of only 1.3%, it precisely shows a very exact
anticipation of the level as well as a correct prediction of the extremum, as can be seen
in graph 17.72
Graph 17: ARIMA Rent Model Forecast Outcomes – Nuremberg
7.6
7.6
7.2
7.2
6.8
6.8
6.4
6.4
6.0
6.0
5.6
5.6
5.2
5.2
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Nuremberg
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Nuremberg
x Stuttgart:
According to the output of the correlogram and by considering the performance
measures for the tested ARIMA specifications, I apply an ARIMA(4,1,0) process for
all Stuttgart forecasting models.73 Again, the performance measures indicate good and
relatively accurate forecasts for the one to three year forecasting models. The four- and
five-year forecasting models deliver much poorer precision.74 The coefficient
estimations for the two ARIMA(4,1,0) are very stable, displaying significantly positive
coefficients for the AR(1) as well as the AR(3) terms and negative ones for the AR(2),
and AR(4) terms, although only the AR(4) coefficient is significantly different from
zero.
The one-year out-of sample forecasting model slightly underestimates the level
of the actual rent in 2006. The reason for this is the lack of anticipation of the
extremum in 2005. The two-year forecast demonstrates a very precise anticipation of
72
The figures representing the respective MAPE performance measures are taken from table 22 in the
appendix.
73
74
This is illustrated in table 25 in the appendix.
The performance measures of the Stuttgart’s ARIMA specifications are shown in table 24 in the
appendix.
65
the decrease in rent level in 2005. Again, the extremum is not recognized and thus the
rent level for 2006 is predicted too low.
Table 9: ARIMA Rent Model Forecast Outcomes – Stuttgart
Stuttgart
Actual series
1998
1999
2000
2001
2002
2003
2004
2005
2006
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.5
One-year
Two-year
ARIMA(4,1,0) ARIMA(4,1,0)
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.3
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.2
Three-year
Four-year
Five-year
ARIMA(4,1,0)
ARIMA(4,1,0)
ARIMA(4,1,0)
7.2
7.0
7.2
7.7
8.0
7.9
7.9
7.7
7.4
7.2
7.0
7.2
7.7
8.0
8.4
8.6
8.5
8.4
7.2
7.0
7.2
7.7
8.1
8.5
8.7
8.7
8.6
The same is the case for the three-year forecast, even though the 2006 level is
only slightly underestimated. This is due to the fact that the drop in the actual rent
series in 2004 and 2005 is not predicted to its full extent. The four- and the five-year
level forecasts both overestimate the true values by about 11% on average. This can be
explained by the fact that the peak in 2002 is not predicted correctly. Both models set
the peak in 2004 instead, as can be seen in graph 18. Afterward, the models predict a
drop in rents failing to anticipate the extremum in 2005
Graph 18: ARIMA Rent Model Forecast Outcomes – Stuttgart
11
11
10
10
9
9
8
8
7
7
6
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
.
Three-year
Stuttgart
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Stuttgart
66
5.1.3. GARCH models: Construction, estimation, and forecasting
In this subchapter, I enrich the ARIMA forecasting models of two cities, namely
Frankfurt and Munich, with GARCH processes. These processes build the variance
equation in these combined ARIMA(p,i,q)GARCH(q,p) models. Since both cities
demonstrate an enormous rent increase75 and thus increased volatility throughout the
last years, a GARCH specification is chosen to try to improve the forecasts. For both
cities the one- up to five-year forecasts of the best fitting ARIMA-GARCH
specifications are shown and interpreted. Additionally, the results are compared to the
outcomes of the simple ARIMA forecasting models.
x Frankfurt:
By considering the performance measures for the tested ARIMA-GARCH
specifications, I apply an ARIMA(4,1,0)GARCH(0,1) process for the Frankfurt oneyear forecasting model. The specifications for the two-, the three-, and the five-year
forecasting models are ARIMA(4,1,1)GARCH(0,1). Finally, the specification for the
four-year forecasting model is ARIMA(4,1,1)GARCH(1,1). Again, the performance
measures for the one- to three-year forecasting models point to good and relatively
accurate forecasts. With the ARIMA-GARCH specification this is also true for the
four-year forecasting model since its performance measures have improved greatly.76
Table 10: GARCH Rent Model Forecast Outcomes – Frankfurt
Frankfurt
One-year
Two-year
ARIMA(4,1,0) ARIMA(4,1,1)
Actual series GARCH (0,1) GARCH (0,1)
1998
1999
2000
2001
2002
2003
2004
2005
2006
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.5
75
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.8
14.4
16.4
18.3
19.3
18.0
14.5
12.5
11.9
11.9
Three-year
ARIMA(4,1,1)
GARCH (0,1)
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.2
13.2
Four-year
ARIMA(4,1,1)
GARCH (1,1)
14.4
16.4
18.3
19.3
18.0
15.6
14.2
12.9
12.4
Five-year
ARIMA(4,1,1)
GARCH (0,1)
14.4
16.4
18.3
19.3
20.0
19.7
19.1
18.6
18.2
Both cities' rent levels skyrocketed due to their economic focuses on New Economy and financial
companies. This bubble is called the "Internet bubble" or "New Economy Bubble" in colloquial
language.
76
Refer to table 11.
67
The one-year forecasting model (ARIMA(4,1,0)GARCH(0,1)) still presents an
overestimation of the actual level of around 2.5%. The two-year forecasts however
clearly show an underestimation in both years by about 5%. Compared to the
forecasting outcomes of the simple ARIMA model, this specification is clearly
inferior. This can also be observed by looking at the respective performance measures
in table 11.
Graph 19: GARCH Rent Model Forecast Outcomes – Frankfurt
20
22
19
20
18
17
18
16
16
15
14
14
13
12
12
11
10
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Thre-year
Frankfurt
Four-year
Five-year
Frankfurt
Table 11: Comparison: Univariate Rent Models – Frankfurt
ARIMA Model
RMSE
MAPE
ARIMA-GARCH Model
RMSE
MAPE
One-year
0.318
2.544
0.258
2.062
Two-year
0.210
1.615
0.585
4.674
Three-year
0.797
4.291
0.454
2.844
Four-year
2.743
20.975
1.029
6.361
Five-year
5.534
39.971
5.356
38.721
68
The results of the three- and the four-year forecasting models, however, visibly
outperform the forecasting power of the respective simple ARIMA model. Especially
the four-year model is more appropriate in predicting the rent drop and thus the actual
level. Again, the drop in 2002 and 2003 is underestimated, but not to the extent that
the ARIMA model predicted. However, the total rent decrease until 2006 is well
anticipated with respect to the whole time frame, as can be seen in graph 19. The fiveyear ARIMA-GARCH forecasting model also provides a better performance than its
ARIMA counterpart, although this time the improvement is only marginal.
x Munich:
Table 12: GARCH Rent Model Forecast Outcomes – Munich
Munich
One-year
Two-year
ARIMA(2,2,2) ARIMA(2,2,2)
Actual series GARCH (1,1) GARCH (1,1)
1998
1999
2000
2001
2002
2003
2004
2005
2006
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.0
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
6.9
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.1
6.8
Three-year
ARIMA(1,2,2)
GARCH (1,1)
8.3
8.8
10.9
12.5
10.8
8.9
7.9
7.4
6.9
Four-year
ARIMA(1,2,2)
GARCH (1,1)
8.3
8.8
10.9
12.5
10.8
8.9
8.0
7.6
7.3
Five-year
ARIMA(2,2,2)
GARCH (1,1)
8.3
8.8
10.9
12.5
13.0
13.7
13.9
14.1
14.2
For the Munich one-, two-, and five-year forecasting models, I apply
ARIMA(2,2,2)GARCH(1,1) specifications with regard to the performance measures.
The three- and four-year forecasting models are ARIMA(1,2,2)GARCH(1,1). The
performance measures for the one- to three-year forecasting models point to good and
relatively accurate forecasts. Again, this is also true for the four-year forecasting
model since its performance measure has improved greatly.77
The one- and the two-year forecasting models (ARIMA(2,2,2)GARCH(1,1))
show a slight underestimation of the actual level. Compared to the simple ARIMA
model, this model demonstrates minor inferiority.78 On the other hand, the results of
the three- and the four-year forecasting models evidently outperform their respective
77
These performance measures can be observed in table 13.
78
This can also be observed by looking at the respective performance measures in table 13.
69
simple ARIMA counterpart. Again, the four-year model yields to a major
improvement in forecasting power. Only small deviations represented by slight level
overestimations can be observed. The Munich five-year ARIMA-GARCH forecasting
model also provides a better performance than its ARIMA counterpart. This time,
compared to the Frankfurt five-year model, the improvement is significant. However,
it is still a very poor forecast, failing to anticipate the actual rent drop in the
forecasting period and showing an average deviation of 70%, which is illustrated by
Graph 20.
Graph 20: GARCH Rent Model Forecast Outcomes – Munich
13
15
14
12
13
11
12
10
11
9
10
9
8
8
7
7
6
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Four-year
Five-year
Munich
Three-year
Munich
Table 13: Comparison: Univariate Rent Models – Munich
ARIMA Model
RMSE
MAPE
ARIMA-GARCH Model
RMSE
MAPE
One-year
0.000
0.003
0.065
0.925
Two-year
0.058
0.761
0.159
1.985
Three-year
0.190
2.328
0.127
1.635
Four-year
0.807
10.019
0.261
3.133
Five-year
7.722
93.673
5.729
70.154
70
5.1.4. Conclusion
To construct ARIMA models for city rent time series, all series had to first be
differenced to achieve to stationarity. Essen as well as Munich even had to be
differenced twice.
Most differenced city series can be represented by AR(4) processes. However,
for some cities AR(2) as well as AR(3) processes seem to be appropriate. Munich's
three- and four-year forecasting models are a further exception, showing only an
AR(1) process. Moreover, Munich is the only city where the adding of MA(q)
processes appears reasonable throughout all of the forecasting models. MA(1)
processes can furthermore be found in some of the best fitting forecasting models for
Frankfurt, Nuremberg, and Dusseldorf.
There is a general pattern for the outcomes of the ARIMA forecasting models
throughout all of the cities. One could say that, according to the respective
performance measures, the one- to three-year forecasting models predict the rent level
very precisely. Furthermore, the extrema and thus peaks and troughs are mostly well
estimated; hence, it follows that also the direction of the rent level development is
projected very well. On the other hand, the four- and the five-year models demonstrate
weaknesses, especially in anticipating the correct rent level. This general pattern seems
to follow the theoretical logic that ARIMA models lose predicting power the longer
the forecasting horizon becomes.79
Nevertheless, there are exceptions from this general pattern. The forecasts for
Dusseldorf are permanently misleading, except the two-year model's forecasts. For
Nuremberg the opposite is true, showing permanently precise predictions of the rent
level. The same is valid for Essen, where the steady development of the rent series is
also well predicted throughout all of the forecasting models.
Due to the effects of the New Economy boom such as increased rent volatility,
which can be observed especially in the rent series of Frankfurt and Munich, GARCH
models were applied. The outcomes of these forecasting models show out
performances in the longer run. Especially for both sample cities, the four-year
forecasting model is clearly improved and thus by far superior to the forecasts of the
simple ARIMA specifications. It seems that for cities which show characteristics of
79
For more details refer to chapter 3.3.5.
71
increased rent volatility, better forecasts in the longer run can be achieved by including
GARCH specifications in the forecasting models.
5.2. Multivariate regression models
Chapter 5.2 is organized as follows. Firstly, a range of possible explanatory variables
is analyzed regarding stationarity. Then a correlation analysis is conducted between
the stationary series of these variables and the first differenced rent series. In chapter
5.2.2 single equation panel models for the different forecasting horizons are estimated
and their outcomes are discussed briefly. The rent series are then forecasted for each
city using these models. Finally, the forecasting outcomes for the one-year to five-year
models are shown and interpreted.
5.2.1. Explanatory variables analysis
In this subchapter I choose to investigate indicators from different sources which the
general literature considers as proxies for office space demand or supply or as
generally influential on the rent development. First, I run panel unit root tests for the
levels of the combined possibly explanatory series taken from the Feri Real Estate
Database. These time series are indicators directly taken from the broader real estate
markets. The results show non-stationarity. Hence, these series are first differenced
and I conduct the panel unit root tests one more time. Now, all series appear to be
stationary.80 For possibly explanatory series, which are measures of the state of the
economy on a national basis and drawn from Thomson Datastream, I apply common
unit root tests which demonstrate the same pattern for all variables. On the one hand,
the level series are non-stationary. On the other hand, the first differences are
stationary.81
80
The same examination steps were executed for the shortened and combined city rent series with the
same outcome. All test results are illustrated in tables 6 to 9 in the appendix. For the level tests I added
a constant and a trend. For the first and second difference tests, I removed the exogenous trend
variable because of the detrended series. Automatic eviews lag length criteria were implemented.
Series of the different sub samples brought very similar results. Results are not reported, however,
they are available upon request.
81
Unit root tests examining the stationarity of these series are depicted in tables 4 and 5 in the
appendix.
72
With the first differences of the combined series I now conduct a correlation
analysis of the rent series and the potentially explanatory variables. The results can be
observed in table 14.
Table 14: Correlation analysis: Rent vs. potential explanatory variables82
d(Rent)
d(Office Employees)
d(Office space inventory) (-1)
d(Vacancy; Office space)
d(Gross value added; Public & private services)
d(Gross value added; Financial & other services)
d(Consumer Price Index, Germany) (-2)
d(Construction Price Index-new office buildings, Germany) (-2)
d(Germany Interbank 12 mth (LDN: BBA) - offered rate) (-1)
d(Germany (DEM) IR Swap 10 Year - middle rate) (-3)
0.4244*
-0.3823*
-0.5115*
0.1869
-0.2183*
-0.2176*
0.3248*
-0.3071*
There is a positive correlation between the first difference of "Office Employees"
and the first difference of the rent series. The coefficient is clearly positive around 0.4,
with the asterisk denoting those values significantly different from zero on the 1%
level. This could be expected since, for instance, a positive change in "Office
Employees" such as a positive impulse from the demand side for office space should
lead to increasing rents ceteris paribus. The pattern in the opposite direction is true for
the correlation between the first difference of "Office Space Inventories" with lag 1
such as a supply impulse and the first difference of the rent series. Even though this
relation is also valid when applying the variable with lag 0, the negative correlation
coefficient around 0.4 is higher and more significantly different from zero when lag 1
is employed.83 Thus, we can observe a forerunner of this explanatory variable, and
hence a clearly causal relationship, as could be expected. Since the necessary data is
only available on an aggregated annual basis for many of the other variables such a
clear causal relation cannot be detected. Most influences are seemingly
contemporaneous.84 This can be observed in the correlation between the first
difference of "Vacancy, Office Space" and the first difference of the rent series, which
displays a highly significant negative coefficient of around -0.5. The negative relation
82
The expression d(.) means that the expression within the brackets is first differenced.
83
As for this variable, lags of some other variables also deliver more significant correlations with the
rent change than their specification at lag zero, as can be observed in the remainder of this subchapter.
84
This is one reason why I did not apply VAR and VEC models, since this fact led to inferior
forecasting equations according to my tests.
73
could be expected, since an increasing office space vacancy rate sets pressure on the
rents, which was shown by many earlier studies.85 For the correlation between the first
difference of "Gross Value Added; Public & Private Services", and the first difference
of the rent series, a positive coefficient is again calculated. However, it is only
significantly different from zero on the 10% level. Hence, this demand proxy does not
seem to have a high influence on the development of office rents. I suppose that this
demand proxy is not specific enough for explaining rent level changes. The first
difference of "Gross Value Added; Financial and other Services", furthermore, has no
explanatory power for office rents at all. The correlation coefficient is not significantly
different from zero. Interestingly, the first differences of both price indicators chosen
do show negative correlation coefficients. The correlation between the first difference
of "Consumer Price Index, Germany" with a chosen lag 2 and the first difference of
the rent series is -0.2. The same is true for the first difference "Construction Price
Index-new office buildings, Germany" with a chosen lag 2. Thus, a rising general price
level indicates a decreasing rent level two years later for Germany. Since the rent level
declined throughout the chosen period as can be seen in chapter 5.1.1 and the inflation
was low but permanently positive in this time frame, the decoupling and opposite
behavior of both series according to the outcomes of the correlation analysis makes
sense. The question, however, is whether this pattern is stable. Furthermore, two
different interest rates were tested regarding their influence on rent development.
There is a positive correlation between the first difference of "Germany Interbank 12
mth (LDN: BBA) - offered rate" with a chosen lag of 1 and the first difference of the
rent series. The coefficient is clearly positive, around 0.3, and significantly different
from zero on the 1% level. A negative correlation between the first difference of
"Germany (DEM) IR Swap 10 Year - middle rate" with lag 3 and the first difference of
the rent series is detected. It is highly significant, with a correlation coefficient of -0.3.
5.2.2. Model construction and estimation
Referring to earlier studies already presented in chapter 2, the first differences of the
variables "Office Employees" and "Office Space Inventories" with lag 1 as proxies for
demand and supply change in the real estate office markets were set as the basic
explanatory variables. On the one hand, both variables are highly correlated with the
respective first differenced rent series according to chapter 5.2.1. On the other hand, I
follow the logic of a price mechanism and enter a demand as well as a supply factor in
85
Some of these studies have already been discussed in chapter 2.
74
the estimation equation. After setting up this basic equation, I analyze all possible
combinations with the other variables regarded as influential according to the
correlation examinations in chapter 5.2.1. However, none of these combinations
achieved a significant improvement in the adjusted R² and the applied performance
measures. On the other hand, many of the other included variables appeared to be
insignificant, considering their t-values.86 Their inclusion sometimes also resulted in
spurious outcomes caused by multicollinearity.
In the end, the best forecasting performance measures and the highest adjusted R²
equal to 0.6 resulted from the parsimonious model using only the first differences of
"Office Employees" and "Office Space Inventories"87 to explain the change in rent
level.88 Thus, there is the combination of only one demand variable and one supply
variable which is sufficient to accurately forecast the development of the rent level
within the nine German office markets included in this investigation.89 All included
panel series have the starting value 1992.
There is a clear pattern regarding the coefficients of the independent variables
throughout the different forecasting models. The coefficients of "Office Employees"
are always significantly positive. The coefficients can be found in a range between 1.7
and 2.1, with an increasing tendency dependent on the sample size. The coefficients of
lag 1 of "Office Space Inventories", however, are always negative and significantly
different from zero. Here, the range is between -0.9 to -0.4, again increasing with the
sample size. These results are depicted in table 26 in the appendix.
86
This finding was also recognized when the first difference of the vacancy rate was included in the
equation. According to my correlation analysis and seminal literature, the vacancy rate should have
played an important role. However, in my study it does not deliver an improvement in the performance
measures. On the other hand, for some applied samples, this variable's coefficients display values
insignificantly different from zero.
87
Lag 1 of "Office space inventories" is employed according to the correlation analysis.
88
Due to first order autocorrelation - determined by the Durbin-Watson statistics - this estimation was
corrected according to the Cochrane & Orcutt (1949) procedure.
89
A test for panel cointegration demonstrated that the hypothesis of a cointegrated relation between
the series has to be rejected. Thus, no Error Correction Model is applied. The exercised multivariate
models are single equation panel models in their first difference representation.
75
5.2.3. Discussion of the city rent series forecasts
x Cologne:
Table 15: Multivariate Regression Rent Model Forecast Outcomes – Cologne
1998
1999
2000
2001
2002
2003
2004
2005
2006
Cologne
One-year
Two-year
Three-year
Four-year
Five-year
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.8
7.5
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.8
7.6
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.9
7.8
8.4
8.7
9.1
9.4
9.1
8.4
7.6
7.2
7.0
8.4
8.7
9.1
9.4
9.1
8.4
7.6
7.2
7.0
8.4
8.7
9.1
9.4
9.5
9.0
8.3
8.0
7.9
Graph 21: Multivariate Regression Rent Model Forecast Outcomes – Cologne
11
11.0
10.5
10
10.0
9.5
9
9.0
8
8.5
8.0
7
7.5
7.0
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Cologne
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Cologne
According to table 15 the one-year Panel forecasting model for the Cologne rent
series provides a prediction that correctly anticipates the continued downward
development in 2006, but the level is a bit overestimated. The same pattern can be
found in the forecasts of the two-year model. They also show the right direction for
both years with a slight overestimation. The three-year forecasting model illustrates
the actual downward development of the rent level series in the years 2004 until 2006;
however, it fails to predict the actual level in 2006 by about 7%. This deviation is
caused by the exaggerated rent drop prediction for the year 2004. The same is true for
the four-year forecast. The prediction for the value in 2003 is still very precise,
76
accurately anticipating the drop of almost 8% within that year. However, again the
economic variables predicted a more significant decline in rent level for 2004 than was
actually the case. The five-year forecasting model shows a permanent overestimation
of the predicted rent values for the total forecasting horizon. This is because the
extremum in 2001 is not correctly anticipated and thus the predicted drop starts one
year too late. One can also observe these patterns in graph 21.
x Dusseldorf:
Table 16: Multivariate Regression Rent Model Forecast Outcomes – Dusseldorf
1998
1999
2000
2001
2002
2003
2004
2005
2006
Dusseldorf
One-year
Two-year
Three-year
Four-year
Five-year
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.5
7.6
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.5
7.4
11.2
11.5
11.8
11.9
12.0
10.7
8.8
6.5
6.4
11.2
11.5
11.8
11.9
12.0
10.7
9.6
7.3
7.3
11.2
11.5
11.8
11.9
12.0
11.2
10.2
7.7
7.7
11.2
11.5
11.8
11.9
11.6
10.8
9.9
7.5
7.6
The Dusseldorf one-year forecasting model slightly underestimates the level of
the actual rent in 2006 by not tracking the trough in rent level in 2005. The two-year
forecasting model predicts rent levels at about 15% below the actual outcomes. Thus,
according to the economic variables, the rent drop in the actual values should have
been stronger. However, by considering the three- and the four-year models, one can
again observe more precise rent level predictions for 2005 and 2006, which is due to
the models' anticipation of a smaller rent drop than actually occurred in 2003 and
2004. One could interpret the situation to mean that the economic conditions were
anticipated in advance. Especially the large increase in office space inventory in 2004
was already priced in the market in 2003.90 Finally, the five-year forecasting model
demonstrates excellent rent level predictions for 2005 and 2006. The model presents
the same pattern as the three- and the four-year models. Nevertheless, the five-year
model does not correctly anticipate the rent level peak in 2002 and sets the extremum
one year before. This, in the end, however seems to be economically correct, since the
90
Acording to the model this should not have happened before 2005.
77
long-run level prediction for 2005 and 2006 proves to be very precise, as can also be
observed in graph 22.
Graph 22: Multivariate Regression Rent Model Forecast Outcomes – Dusseldorf
13
13
12
12
11
11
10
10
9
9
8
8
7
7
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Dusseldorf
Three-year
Dusseldorf
x Essen:
Table 17: Multivariate Regression Rent Model Forecast Outcomes – Essen
1998
1999
2000
2001
2002
2003
2004
2005
2006
Essen
One-year
Two-year
Three-year
Four-year
Five-year
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.3
5.3
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.3
5.2
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.2
5.0
5.8
6.1
5.9
5.6
5.5
5.5
5.2
5.0
4.9
5.8
6.1
5.9
5.6
5.5
5.3
5.0
4.8
4.6
5.8
6.1
5.9
5.6
5.4
5.1
4.8
4.7
4.6
The one-year forecast for the Essen rent level series appears to slightly
underestimate the actual market rent; however, the level prediction is still good
according to table 17. The two-year forecasting model demonstrates an average
underestimation of the actual level of about 4%. This deviation increases up to 8%
within the five-year model. Even though the actual market rent only drops slightly in
2002 and 2004, expressing a steady development, the rest of the time the forecasts
permanently decrease, independent of the forecasting horizon. Thus, the longer the
forecasting horizon is, the greater the forecasting deviation is from the actual value in
2006. This implies that, at least in the forecasting periods up to five years in the years
78
after 2002, the rent level in Essen was not completely driven by its economic
fundamentals, as is underlined by graph 23.
Graph 23: Multivariate Regression Rent Model Forecast Outcomes – Essen
6.8
6.8
6.4
6.4
6.0
6.0
5.6
5.6
5.2
5.2
4.8
4.4
4.8
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Three-year
Essen
Five-year
Essen
x Frankfurt:
Table 18: Multivariate Regression Rent Model Forecast Outcomes – Frankfurt
1998
1999
2000
2001
2002
2003
2004
2005
2006
Frankfurt
One-year
Two-year
Three-year
Four-year
Five-year
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.5
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.5
14.4
16.4
18.3
19.3
18.0
14.5
12.5
11.7
11.4
14.4
16.4
18.3
19.3
18.0
14.5
12.6
11.8
11.5
14.4
16.4
18.3
19.3
18.0
16.2
14.8
14.2
14.0
14.4
16.4
18.3
19.3
18.7
17.3
16.0
15.5
15.4
The steady rent development in 2006 is exactly predicted by the Frankfurt oneyear panel forecasting model. This is not the case for the forecasts of the two-year
forecasting model. Instead of stable rent series, the level is predicted too low by about
6% in 2005, dropping further in 2006. The same pattern for the years 2005 and 2006 is
demonstrated in the three-year model, but at least the level drop of 15% in 2004 is
estimated correctly. On the other hand, the level forecasted by the four- and the fiveyear models is too high.91 The tremendous drop of almost 20% in 2003 is only half
anticipated by both models. Furthermore, the five-year model cannot completely
91
This is illustrated in graph 24.
79
reproduce the drop in 2002. One could conclude that the market is not following
economic fundamentals in that period. Actual figures are decreasing too strongly from
2001 until 2004 and stop falling after 2004, showing backlash which is not distinctive
enough for the exaggeration. However, I argue that the starting values for the four- and
the five-year models in 2001 or 2002 respectively are too high and not on an
economically reasonable level. Thus, the market might be out of its long-run
fundamental equilibrium, which leads to forecasting results that deviate significantly
from the actual values. This leads to the hypothesis that the panel model with its
economic determinants works correctly in the long run when the forecasting period
starts at a point where the economic fundamentals determine the actual price to a
greater extent.
Graph 24: Multivariate Regression Rent Model Forecast Outcomes – Frankfurt
20
20
19
19
18
18
17
17
16
16
15
15
14
14
13
13
12
12
11
11
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Frankfurt
Three-year
Frankfurt
x Hamburg:
Table 19: Multivariate Regression Rent Model Forecast Outcomes – Hamburg
1998
1999
2000
2001
2002
2003
2004
2005
2006
Hamburg
One-year
Two-year
Three-year
Four-year
Five-year
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.8
6.8
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.8
7.0
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.6
6.7
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.6
6.7
7.4
7.7
8.2
8.5
8.1
7.5
7.2
7.1
7.3
7.4
7.7
8.2
8.5
8.2
7.8
7.5
7.5
7.7
80
The Hamburg one-year panel forecast represents a slight overestimation of the actual
level. This pattern can also be noticed in every other Hamburg forecasting model, even
though the actual figures show a steady development. The two-year model predicts a
slight downward pattern of the rent level. In the actual market figures there is already
an extremum in 2004, and thus the level in 2005 increases. For 2004 the three-year
model depicts the actual drop very precisely. For the years 2005 and 2006 the same
pattern appears as in the two-year model. For the four- and the five-year models, the
actual rent drops in 2003 and in 2002 are slightly underestimated. Furthermore, both
models also underestimate the drop in 2004. Thus, for both models the final level
prediction in 2006 is too high, as is illustrated in graph 25.
Graph 25: Multivariate Regression Rent Model Forecast Outcomes – Hamburg
10.0
10.0
9.5
9.5
9.0
9.0
8.5
8.5
8.0
8.0
7.5
7.5
7.0
7.0
6.5
6.5
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Hamburg
Three-year
Hamburg
x Leipzig:
Table 20: Multivariate Regression Rent Model Forecast Outcomes – Leipzig
1998
1999
2000
2001
2002
2003
2004
2005
2006
Frankfurt
One-year
Two-year
Three-year
Four-year
Five-year
5.9
5.5
5.1
5.1
4.8
4.7
4.7
4.6
4.7
5.9
5.5
5.1
5.1
4.8
4.7
4.7
4.6
4.7
5.9
5.5
5.1
5.1
4.8
4.7
4.7
4.6
4.7
5.9
5.5
5.1
5.1
4.8
4.7
4.5
4.3
4.4
5.9
5.5
5.1
5.1
4.8
4.7
4.5
4.3
4.3
5.9
5.5
5.1
5.1
5.0
4.9
4.8
4.7
4.8
The Leipzig one- and two-year forecasting models present very precise results.
While the one-year model anticipates the extremum in 2005, displaying the exact level
81
increase, the two-year model firstly predicts the slight downturn in 2005 accurately
and furthermore correctly forecasts the extremum and upturn in 2006. The three-year
model predicts a decrease in the rent level for 2004, although the actual value remains
stable. The downturn which follows in 2005, and the upward development in 2006, is
well anticipated again; however, the level is too low because of the wrong prediction
for 2004.
Graph 26: Multivariate Regression Rent Model Forecast Outcomes – Leipzig
14
14
12
12
10
10
8
8
6
6
4
4
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Leipzig
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Leipzig
The four-year model correctly anticipates the level downturn in 2003. The rest of
the forecasted years demonstrate the same pattern as the three-year model. Finally, the
five-year model also shows a pattern of a rent level decrease followed by an upward
development in 2006. The level is slightly too high due to the underestimation of the
rent level drop in 2002. Subsumed in graph 26, the economic relation seems to work in
Leipzig for the given models and the time period chosen.
x Munich:
The Munich one-year panel model slightly overestimates the drop in rent level in
2006. The opposite is true for the two-year out-of sample forecasting model, where the
drop of 8% is only partially anticipated. This serves as a reason for the level
overestimation in 2006. The three-year model demonstrates the same pattern for the
last two years. Moreover, it very precisely forecasts the 12% rent level drop in 2004.
82
However, the drop of almost 18% in 2003 cannot be completely covered by the fouryear model. The remaining pattern of the following years remains the same as in the
four-year model. Finally, the five-year model shows a drop in rent after 2002.
Nevertheless, the magnitude is far too low.92 This pattern is supported by a prediction
of a rent level increase in 2002, although the actual extremum is already present in
2001. From my point of view, the explanation for the Munich rent level pattern has the
same background as Frankfurt’s. Again, we seem to face an exaggeration in actual rent
level around 2001. Using this year as a starting level, one can see that economic
development cannot explain the total drop in rent. As we will see later on, the rent
level in 2001 is the peak of a bubble far beyond economically reasonable values. If we
start the forecasting period at the peak, this also means starting the forecasts at a time
when the actual price is out of its equilibrium.
Table 21: Multivariate Regression Rent Model Forecast Outcomes – Munich
1998
1999
2000
2001
2002
2003
2004
2005
2006
Munich
One-year
Two-year
Three-year
Four-year
Five-year
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.0
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
6.8
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.6
7.4
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.7
7.4
8.3
8.8
10.9
12.5
10.8
9.4
8.4
8.3
8.1
8.3
8.8
10.9
12.5
12.7
11.8
11.0
11.0
10.9
Graph 27: Multivariate Regression Rent Model Forecast Outcomes – Munich
13
13
12
12
11
11
10
10
9
9
8
8
7
7
6
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92
Three-year
Munich
This can be seen in table 21 and graph 27.
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Munich
83
x Nuremberg:
Table 22: Multivariate Regression Rent Model Forecast Outcomes – Nuremberg
1998
1999
2000
2001
2002
2003
2004
2005
2006
Nuremberg
One-year
Two-year
Three-year
Four-year
Five-year
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
6.0
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
5.8
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.5
5.6
5.8
6.0
6.4
6.3
5.8
5.7
5.5
5.5
5.5
5.8
6.0
6.4
6.3
5.8
5.4
5.1
5.0
5.1
5.8
6.0
6.4
6.3
6.0
5.6
5.4
5.3
5.4
The one-year forecasting model displays a rent level upturn in 2006. This is
correctly anticipated, but to a degree which is too low. While the two-year model fails
to capture the extremum in 2004 and predicts a decline in 2005, the upward
development in 2006 is covered. The three-year model anticipates the end of the rent
decrease after 2004, but instead of forecasting increasing rent levels, it predicts a
development to the side. The four-year model again shows the pattern with a trough in
2005 and therefore one year too late. Furthermore, the actual rent decreases in 2003
and 2004 are overestimated, leading afterward to rent levels too low, which results in a
deviation of 15% in 2006. The same pattern appears for the five-year forecasting
model; however, the level is higher since the downturn in 2002 is underestimated
before the drop in 2003 is overestimated. It seems that the Nuremberg market is not
working completely according to economic fundamentals, although their determining
power can still be stated.
Graph 28: Multivariate Regression Rent Model Forecast Outcomes – Nuremberg
7.6
7.6
7.2
7.2
6.8
6.8
6.4
6.4
6.0
6.0
5.6
5.6
5.2
5.2
4.8
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Nuremberg
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Nuremberg
84
x Stuttgart:
Table 23: Multivariate Regression Rent Model Forecast Outcomes – Stuttgart
1998
1999
2000
2001
2002
2003
2004
2005
2006
Stuttgart
One-year
Two-year
Three-year
Four-year
Five-year
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.5
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.1
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.6
7.4
7.2
7.0
7.2
7.7
8.0
7.9
7.5
7.4
7.2
7.2
7.0
7.2
7.7
8.0
7.6
7.2
7.1
7.0
7.2
7.0
7.2
7.7
7.9
7.6
7.2
7.2
7.1
The one- to five-year forecasting models for the Stuttgart rent level series all lead
to a level underestimation for the year 2006. The main reason is the failure to predict
the extremum in 2005 and hence, the absence of the actual rent level upturn in 2006.
Thus, the level in the one-year model is predicted 5% too low. The level prediction in
the two-year model is better since this model does not capture the actual decrease in
rent level in 2005. The three-year model precisely anticipates the rent level
development in 2004 and 2005. Nevertheless, again, the level increase in 2006 is not
predicted. The four- and the five-year models do not track the rent level in 2006 by an
even greater margin, as illustrated by graph 29. This is due to fact that the downturn in
2003 is overestimated. Worthy of mention, however, is the good anticipation of the
peak in 2002.
Graph 29: Multivariate Regression Rent Model Forecast Outcomes – Stuttgart
11
11
10
10
9
9
8
8
7
7
6
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Stuttgart
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Stuttgart
85
5.2.4. Conclusion
This subchapter applied multivariate regression models to precisely forecast the rent
level development of nine German office markets. After a correlation analysis of the
first differenced panel rent series with the first differences of several potentially
explanatory panel variables, it turned out that the construction of a parsimonious
model with a single demand and a single supply variable as explanatory variables is
sufficient. These included variables are the first differences in the panel data series
"Office Employees" and "Office Space Inventories". With an adjusted R² of around
60% this model can explain more than half of the variance of the first differenced
panel rent series.
A general finding for the nine German office markets examined is that the rent
level is mainly determined by the market's economic fundamentals. There exists a
clear relationship between the change in rent level and the development of "Office
Employees" as a demand variable and the development of "Office Space Inventories"
as a supply variable. Extrema in the rent development and thus the direction are
forecasted correctly most of the time. In the case where they are not, the developments
can mostly be observed one period afterward.93 Furthermore, there are precise
predictions of the rent level.
However, there are exceptions. For most of the cities the forecast outcomes
deviate more and more from the actual rent level, the longer the forecasting period is.
Good examples for this pattern are Frankfurt and Munich. The reason for this already
indicated in the single cities' rent development analysis is that the four-and five-year
forecasts of these cities start in a time of economically unreasonable rent levels, i.e., in
the aftermath of the New Economy boom. Thus, my conclusion is that it is not a
general problem that the four- and five-year multivariate regression forecasting models
perform poorly compared to the short-run models. In fact, it is more a problem of the
starting value of the models' forecasts. In chapter 5.4, I show that a forecast with a
starting value in a period of economically reasonable rent levels delivers improved
long-term forecasts. Another finding is that exaggerations cannot be captured by a
model consisting only of explanatory variables replicating the real economy.
93
This is not a general sign of a misspecification of the model with regard to lag structure, since most
of the city forecasts do not capture one of their extrema within the forecasting period, but meet another
one exactly. This imprecision, however, could be attributed to the high aggregation of annual data.
86
5.3. Comparison of univariate and multivariate models
This subchapter compares the one-year to five-year rent level forecasting results of the
best fitting univariate models with those of the respective multivariate models. This is
conducted for each city individually by evaluating the performance measures
combined with an examination and direct comparison of the predicted rent values.
Since for Leipzig no univariate estimation could be conducted, I can only compare the
remaining eight German office markets. The subchapter closes with conclusions on the
individual models' appropriateness and best application.
5.3.1. Comparison and interpretations
x Cologne:
Table 24: Rent Forecast Outcomes -Cologne- Comparison Univariate vs. Multivariate Models
Univariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.8
7.5
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.8
7.7
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.9
7.8
8.4
8.7
9.1
9.4
9.1
8.4
7.9
7.5
7.4
8.4
8.7
9.1
9.4
9.1
8.8
8.6
8.4
8.3
8.4
8.7
9.1
9.4
9.5
9.6
9.5
9.3
9.2
Multivariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.8
7.5
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.8
7.6
8.4
8.7
9.1
9.4
9.1
8.4
8.1
7.9
7.8
8.4
8.7
9.1
9.4
9.1
8.4
7.6
7.2
7.0
8.4
8.7
9.1
9.4
9.1
8.4
7.6
7.2
7.0
8.4
8.7
9.1
9.4
9.5
9.0
8.3
8.0
7.9
The comparison of the Cologne univariate and multivariate models shows that
the four- and five-year multivariate forecasting models are superior with regard to the
respective univariate models. The same is true for the one-year models. On the other
hand, the two- as well as the three-year univariate models demonstrates dominance.
This is proved by the forecast rent level figures and their respective direction pattern,
87
which are depicted in table 24. Furthermore, this can be stated by the performance
measures in table 25. Hence, for Cologne there is not a dominant forecasting model,
but one can see the tendency of the multivariate specifications to be dominant in the
longer run, whereas the short run, up to the three-year model, shows a mixed picture.
Table 25: Rent Performance Measure Comparison – Cologne
Univariate Model
RMSE
MAPE
Multivariate Model
RMSE
MAPE
One-year
0.159
2.125
0.113
1.504
Two-year
0.213
2.447
0.216
2.555
Three-year
0.201
2.442
0.575
7.350
Four-year
0.597
7.369
0.453
5.013
Five-year
1.327
15.714
0.404
4.459
x Dusseldorf:
Table 26: Rent Forecast Outcomes -Dusseldorf- Comparison Univariate vs. Multivariate Models
Univariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.5
7.6
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.5
6.8
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.8
7.6
11.2
11.5
11.8
11.9
12.0
10.7
10.0
9.7
10.0
11.2
11.5
11.8
11.9
12.0
12.0
12.1
12.1
12.1
11.2
11.5
11.8
11.9
11.9
12.0
12.0
12.0
12.0
Multivariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.5
7.6
11.2
11.5
11.8
11.9
12.0
10.7
8.8
7.5
7.4
11.2
11.5
11.8
11.9
12.0
10.7
8.8
6.5
6.4
11.2
11.5
11.8
11.9
12.0
10.7
9.6
7.3
7.3
11.2
11.5
11.8
11.9
12.0
11.2
10.2
7.7
7.7
11.2
11.5
11.8
11.9
11.6
10.8
9.9
7.5
7.6
88
For Dusseldorf the multivariate models seem to outperform the univariate models
regarding rent development prediction for every forecasting horizon except for the
two-year horizon, as can be seen in table 26. Here, according to the performance
measures in table 27 the multivariate forecasting model is clearly inferior. Analyzing
the three- to five-year models shows that the multivariate models very precisely
forecast the actual rent level while the univariate model completely fails to track the
drop in rent after 2002 and thus offers entirely misleading rent level predictions. An
explanation for the poor performance of the ARIMA model may be that the Dusseldorf
market faces an “unexpected” extraordinarily large “Office Space Inventory” increase.
Table 27: Rent Performance Measure Comparison – Dusseldorf
Univariate Model
RMSE
MAPE
Multivariate Model
RMSE
MAPE
One-year
0.766
10.073
0.183
2.406
Two-year
0.242
2.465
1.105
14.568
Three-year
2.017
25.077
0.495
5.124
Four-year
3.638
42.209
0.739
5.848
Five-year
3.092
32.122
0.534
3.527
x Essen:
A completely different picture can be observed for the Essen forecasting models.
Here, all univariate models outperform their multivariate counterparts, as illustrated in
tables 28 and 29. Whereas the models based on economic fundamentals seem to
underestimate the actual rent levels to an increasing extent over time, the univariate
models, most of the time, give very accurate forecasts. For Essen, technical models
seem to be more appropriate to achieve good forecasting results. However, the
deviations of the forecasts of the multivariate models are not extraordinarily high
compared to the relative performance measures of other cities. Thus, these forecasts
are not completely misleading.
89
Table 28: Rent Forecast Outcomes -Essen- Comparison Univariate vs. Multivariate Models
Univariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.3
5.3
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.3
5.3
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.2
5.1
5.8
6.1
5.9
5.6
5.5
5.5
5.4
5.3
5.2
5.8
6.1
5.9
5.6
5.5
5.4
5.2
5.1
4.9
5.8
6.1
5.9
5.6
5.7
5.6
5.3
5.3
5.2
Multivariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.3
5.3
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.3
5.2
5.8
6.1
5.9
5.6
5.5
5.5
5.3
5.2
5.0
5.8
6.1
5.9
5.6
5.5
5.5
5.2
5.0
4.9
5.8
6.1
5.9
5.6
5.5
5.3
5.0
4.8
4.6
5.8
6.1
5.9
5.6
5.4
5.1
4.8
4.7
4.6
Table 29: Rent Performance Measure Comparison – Essen
Univariate Model
RMSE
MAPE
Multivariate Model
RMSE
MAPE
One-year
0.019
0.364
0.134
2.523
Two-year
0.165
3.097
0.215
3.703
Three-year
0.074
1.269
0.302
5.056
Four-year
0.236
3.914
0.450
7.863
Five-year
0.125
1.799
0.484
8.371
x Frankfurt:
For Frankfurt the multivariate model works best in the very short- and the very
long run, where it clearly outperforms the univariate models. However, for the two- to
four-year models, the univariate specifications generate superior results, as table 30
and table 31 prove.94
94
The four-year univariate model is an ARMIA-GARCH specification. While this model is superior to
the four-year multivariate model, the four-year ARIMA model in this place would clearly be inferior.
90
Table 30: Rent Forecast Outcomes -Frankfurt- Comparison Univariate vs. Multivariate Models
Univariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.5
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.8
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.2
12.6
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.2
13.2
14.4
16.4
18.3
19.3
18.0
15.6
14.2
12.9
12.4
14.4
16.4
18.3
19.3
20.0
19.7
19.1
18.6
18.2
Multivariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.5
14.4
16.4
18.3
19.3
18.0
14.5
12.5
12.5
12.5
14.4
16.4
18.3
19.3
18.0
14.5
12.5
11.7
11.4
14.4
16.4
18.3
19.3
18.0
14.5
12.6
11.8
11.5
14.4
16.4
18.3
19.3
18.0
16.2
14.8
14.2
14.0
14.4
16.4
18.3
19.3
18.7
17.3
16.0
15.5
15.4
Table 31: Rent Performance Measure Comparison – Frankfurt
Univariate Model
RMSE
MAPE
Multivariate Model
RMSE
MAPE
One-year
0.318
2.544
0.036
0.291
Two-year
0.210
1.615
0.934
7.365
Three-year
0.454
2.844
0.680
4.553
Four-year
1.029
6.361
1.823
13.913
Five-year
5.356
38.721
2.748
19.612
x Hamburg:
For rent level prediction in Hamburg, the multivariate models almost
permanently generate the best results. Only the two-year univariate forecasting model
outperforms its counterpart, as can be seen in tables 32 and 33. Nevertheless, the tables
also show that the predicted rent figures and the respective performance measures for
the one- to three-year models are very similar. Thus, there is only a clear pattern for
the four- and five-year models, where the multivariate specifications prove dominance.
91
Table 32: Rent Forecast Outcomes -Hamburg- Comparison Univariate vs. Multivariate Models
Univariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.8
6.8
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.8
7.1
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.6
6.7
7.4
7.7
8.2
8.5
8.1
7.2
6.6
6.5
6.7
7.4
7.7
8.2
8.5
8.1
7.7
7.4
7.4
7.4
7.4
7.7
8.2
8.5
8.6
8.6
8.6
8.5
8.5
Multivariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.8
6.8
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.8
7.0
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.6
6.7
7.4
7.7
8.2
8.5
8.1
7.2
6.7
6.6
6.7
7.4
7.7
8.2
8.5
8.1
7.5
7.2
7.1
7.3
7.4
7.7
8.2
8.5
8.2
7.8
7.5
7.5
7.7
Table 33: Rent Performance Measure Comparison – Hamburg
Univariate Model
RMSE
MAPE
Multivariate Model
RMSE
MAPE
One-year
0.305
4.480
0.208
3.055
Two-year
0.139
1.826
0.176
2.415
Three-year
0.173
2.092
0.115
1.349
Four-year
0.594
8.575
0.397
5.682
Five-year
1.536
20.977
0.657
8.776
x Munich:
The comparison of the Munich univariate and multivariate models demonstrates
that the forecasts of the one- up to the four-year univariate models are clearly superior
in comparison with the multivariate models, as tables 34 and 35 illustrate. The
opposite picture is given by a comparison of the five-year models, where the
multivariate model delivers the better forecasting results concerning the level as well
92
as direction of development. Here, the level is also highly exaggerated; however, the
model captures the extremum and thus, on average, the right direction by at least
slightly retracing the actual rent level drop at least slightly.
Table 34: Rent Forecast Outcomes -Munich- Comparison Univariate vs. Multivariate Models
Univariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.0
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.0
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.1
8.3
8.8
10.9
12.5
10.8
8.9
7.9
7.4
6.9
8.3
8.8
10.9
12.5
10.8
8.9
8.0
7.6
7.3
8.3
8.8
10.9
12.5
13.0
13.7
13.9
14.1
14.2
Multivariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
7.0
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.2
6.8
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.6
7.4
8.3
8.8
10.9
12.5
10.8
8.9
7.8
7.7
7.4
8.3
8.8
10.9
12.5
10.8
9.4
8.4
8.3
8.1
8.3
8.8
10.9
12.5
12.7
11.8
11.0
11.0
10.9
Table 35: Rent Performance Measure Comparison – Munich
Univariate Model
RMSE
MAPE
Multivariate Model
RMSE
MAPE
One-year
0.000
0.003
0.225
3.211
Two-year
0.058
0.761
0.422
5.930
Three-year
0.127
1.635
0.359
4.168
Four-year
0.261
3.133
0.899
11.384
Five-year
5.729
70.154
3.221
39.929
x Nuremberg:
The Nuremberg univariate models clearly outperform their multivariate
counterparts for all time periods and simultaneously show very precise results as can
be observed in tables 36 and 37. Only the four-year model considerably
93
underestimates the actual rent level. Nevertheless, it is still superior to the multivariate
counterpart.
Table 36: Rent Forecast Outcomes -Nuremberg- Comparison Univariate vs. Multivariate Models
Univariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
6.0
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
6.1
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
6.1
5.8
6.0
6.4
6.3
5.8
5.7
5.5
5.6
5.9
5.8
6.0
6.4
6.3
5.8
5.6
5.3
5.4
5.7
5.8
6.0
6.4
6.3
6.0
5.8
5.6
5.8
6.1
Multivariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
6.0
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.7
5.8
5.8
6.0
6.4
6.3
5.8
5.7
5.6
5.5
5.6
5.8
6.0
6.4
6.3
5.8
5.7
5.5
5.5
5.5
5.8
6.0
6.4
6.3
5.8
5.4
5.1
5.0
5.1
5.8
6.0
6.4
6.3
6.0
5.6
5.4
5.3
5.4
Table 37: Rent Performance Measure Comparison – Nuremberg
Univariate Model
RMSE
MAPE
Multivariate Model
RMSE
MAPE
One-year
0.066
1.097
0.174
2.892
Two-year
0.068
0.919
0.289
4.490
Three-year
0.105
1.708
0.306
4.319
Four-year
0.236
3.740
0.655
10.578
Five-year
0.090
1.282
0.325
4.650
However, the deviations of the forecasts of the multivariate models are not
extraordinarily high compared to the relative performance measures of other cities.
Furthermore, they display the correct direction, although the upswing is predicted one
period too late. Thus, these forecasts are not completely misleading. Following this,
94
the economic fundamentals are also the rent determinants for the Nuremberg rent
development in the long run. Hence, Nuremberg will also be analyzed in the longer
run afterward.
x Stuttgart:
Table 38: Rent Forecast Outcomes -Stuttgart- Comparison Univariate vs. Multivariate Models
Univariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.5
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.3
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.2
7.2
7.0
7.2
7.7
8.0
7.9
7.9
7.7
7.4
7.2
7.0
7.2
7.7
8.0
8.4
8.6
8.5
8.4
7.2
7.0
7.2
7.7
8.1
8.5
8.7
8.7
8.6
Multivariate
Actual series
One-year
Two-year
Three-year
Four-year
Five-year
1998
1999
2000
2001
2002
2003
2004
2005
2006
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.5
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.4
7.1
7.2
7.0
7.2
7.7
8.0
7.9
7.6
7.6
7.4
7.2
7.0
7.2
7.7
8.0
7.9
7.5
7.4
7.2
7.2
7.0
7.2
7.7
8.0
7.6
7.2
7.1
7.0
7.2
7.0
7.2
7.7
7.9
7.6
7.2
7.2
7.1
Table 39: Rent Performance Measure Comparison – Stuttgart
Univariate Model
RMSE
MAPE
Multivariate Model
RMSE
MAPE
One-year
0.240
3.195
0.369
4.925
Two-year
0.177
1.716
0.136
1.739
Three-year
0.244
2.927
0.162
1.707
Four-year
0.900
11.455
0.396
5.015
Five-year
0.954
11.119
0.314
3.813
95
For the Stuttgart forecasting models, again, the pattern demonstrates the
superiority of the multivariate models, the longer the forecasting horizon is. In the
short run there is a mixed picture. The univariate specification is the better one for the
one-year forecasting model. Taking a closer look at table 39, one cannot determine
which model performs better for the two-year specification as the measures show a
mixed picture. While RMSE favors the multivariate model, the opposite is true for
MAPE. However, the outcomes for the two measures show very similar results and
thus are not significantly different from each other.
5.3.2. Conclusion
In this subchapter, I compared the forecasting performances of the best univariate and
multivariate models applied. The comparison was conducted for the selected German
office markets for the one- up to the five-year forecasting horizon, except for Leipzig,
where no univariate investigation could be carried out.
The investigation shows cities where one model permanently or almost
permanently outperforms the other. On the one hand, the univariate model completely
dominates the forecasting performance in Essen and Nuremberg. In Munich that is true
for all but one forecasting horizons. On the other hand, the multivariate model
performs the best for all but one forecasting horizon in Dusseldorf and Hamburg.
To correctly interpret these patterns knowledge about the individual markets is
indispensable. Furthermore, it is very important to also consider the chosen time
frame. Here, the forecasting period chosen (2002 until 2006) is the time directly
following a rent level peak for almost every city selected. Hence, within this period the
rent level is mainly declining. For many cities the four- and five-year models seem to
be inferior. However, this pattern could change by choosing different samples and
different starting values. This point will be considered in the following subchapter.
Besides the pattern of models permanently outperforming other model
specifications in certain cities, I found a different, more general pattern by
distinguishing between short- and long-run forecasting models. If we take the one-year
up to the three-year models for the short-run and the four- and five-year models for the
long-run it becomes obvious that the univariate visibly outperform the multivariate
models in the short run. This is represented by 17 of 24 of the MAPE performance
measures and 16 of 24 of the RMSE performance measures, or about 70%. In the long
96
run the multivariate models dominate in 63% of the cases.95 If we only consider the
five-year models as long run, then multivariate models outperform the univariate in
about 75% of the cases.96
According to this pattern, one could speak of at least of a tendency of
multivariate models to perform better, the longer the time horizon is. In other words,
one can say that in the long run those rent forecasting models which take economic
explanatory variables into consideration, achieve better forecasting results.97
Nevertheless, the picture so far illustrates high deviations for several cities regarding
the outcomes of the five-year forecasting model. This outcome is evident in cities with
high deviations. Here, for the results of the long run forecasts, the drop in rent cannot
be completely anticipated by the models. This becomes extremely obvious for
Frankfurt and Munich, two cities facing an extraordinary rent upswing until 2001 and
a similarly strong downturn afterwards.
5.4. Long-run forecasting models
This subchapter shows and examines multivariate forecasting models for each city that
are able to capture the respective long run rent pattern best. The variables of the
chosen models are the same as for the multivariate models in the shorter run. The only
difference is the increased forecast horizon and thus the reduced estimation sample,
whose exact size only depends on the respective city's forecasting starting value.
To generate these models, each city is analyzed individually in the first
subchapter, in which I present the model whose forecasts show the best performance
measures compared to other long-run forecasting models. The forecasting results are
shown graphically in comparison to the actual rent series, and they are interpreted with
the support of the performance measures MAPE and RMSE.
95
In 10 of 16 cases the MAPE as well as the RMSE performance measures for the multivariate models
outperform those of the univariate specifications.
96
In 6 of 8 cases the MAPE as well as the RMSE performance measures for the multivariate models
outperform those of the univariate specifications.
97
A similar pattern was detected by Hott & Monin (2008) for the US, the UK, Japan, and Switzerland.
97
5.4.1. Determination and interpretation
x Cologne:
To come up with a very precise long-run rent forecasting model for Cologne I
chose the six-year multivariate model. As can be observed in graph 30, the forecasted
values follow the actual rent series very closely. Furthermore, this is underlined by this
model's performance measures. The RMSE is 0.186 and the MAPE is 1.850. Both
figures are considerably lower than their average counterparts for the one- to five-year
models. Even though the extremum in 2001 is predicted one year too late, one can say
according to this model that the Cologne rent series follows its economic fundamentals
in the longer run. The starting point chosen for the model is 2000; thus, the model
displays the first forecast in 2001. In the year of the starting point the Cologne actual
rent series is situated in an upswing, however, not yet at its peak.
Graph 30: Long-Run Rent Model Forecast Outcomes – Cologne
11.0
10.5
10.0
9.5
9.0
8.5
8.0
7.5
7.0
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Six-year
Cologne
x Dusseldorf:
The nine-year out-of sample forecasting model generates very precise forecasts
for the actual rent level in Dusseldorf.98 A RMSE of 0.320 and a MAPE of 2.169, both
far below the average of the one- up to five-year forecasting models' performance
measures, demonstrate that rents in Dusseldorf are mainly determined by demand and
supply factors in the long run. The actual rent series in 1997, the year of the starting
point, is best described as a rent level in a steady state. The small increase until 2002
and the huge drop afterwards are still some years ahead.
98
This can be observed by considering graph 31.
98
Graph 31: Long-Run Rent Model Forecast Outcomes – Dusseldorf
13
12
11
10
9
8
7
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nine-year
Dusseldorf
x Essen:
Graph 32: Long-Run Rent Model Forecast Outcomes – Essen
6.6
6.4
6.2
6.0
5.8
5.6
5.4
5.2
5.0
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Eight-year
Essen
A first look at graph 32, which depicts the Essen eight-year out-of sample rent
forecasting model, gives the impression that the model performs poorly. Since the
extremum in 1999 is not captured and predicted for 2001, the actual rent drop starts
too late within the model, and the forecasts predict a rent level higher than the actual
one throughout almost the entire forecasting horizon. However, by considering the
performance measures RMSE with 0.313 and MAPE with 4.737, the capturing of the
drop in rent level in the new millennium, and the more or less precise level prediction
in 2006, I argue that economic fundamentals also play a major role in the rent
determination in Essen. However, there also seem to be other influences.
99
x Frankfurt:
The Frankfurt nine-year model demonstrates that economic fundamentals more
or less determine the actual rent prices of this city in the long run. The model's starting
value is set in 1997 and therefore before the tremendous increase around the turn of
the millennium. Even though it only narrowly fails to predict the high level of the rent
peak in 2001, the model correctly anticipates the extremum in that year. Furthermore,
it predicts well the tremendous downturn in the years following, even though the level
is overestimated. By 2006, however, the convergence of the actual and the predicted
level has progressed, as illustrated in graph 33. Nevertheless, the performance
measures RMSE = 1.159 and MAPE = 7.034 show that this model is not capable of
delivering exact level forecasts in times of high volatility.
Graph 33: Long-Run Rent Model Forecast Outcomes – Frankfurt
20
19
18
17
16
15
14
13
12
11
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nine-year
Frankfurt
x Hamburg:
The Hamburg nine-year forecasting model generates very precise forecasts. This
is underlined by the outstanding RMSE of 0.144 and a MAPE of 1.709. The model
exactly presents the extrema in 1998 and 2001 and only fails in tracking the one in
2004 by one year, as can be seen in graph 34. One can conclude that the rent
development is determined by its economic fundamentals to a very large extent in the
long run. The starting point is set in 1997, the year before the trough of 1998.
100
Graph 34: Long-Run Rent Model Forecast Outcomes – Hamburg
10.0
9.5
9.0
8.5
8.0
7.5
7.0
6.5
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nine-year
Hamburg
x Leipzig:
Graph 35: Long-Run Rent Model Forecast Outcomes – Leipzig
14
12
10
8
6
4
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Seven-year
Leipzig
With a starting value set in 1999, the actual rents in Leipzig can almost
completely be predicted by their economic fundamentals. This is stressed by an RMSE
of 0.095 and an MAPE of 1.750. Thus, for Leipzig it also turns out to be true that rent
development is determined by demand and supply and that no other factors have
considerable influence. The starting value is set in a time showing relatively stable
rents.
101
x Munich:
The Munich nine-year model demonstrates that the economic fundamentals more
or less determine the actual rent prices of this city in the long run. The model's starting
value is set in 1997 and therefore before the tremendous increase around the turn of
the millennium. Even though it fails in predicting the high level of the rent peak in
2001, the model correctly anticipates the extremum in this year. Furthermore, in the
years following 2003 it again captures the actual level rather closely, as can be
observed in graph 36. Nevertheless, the performance measures RMSE = 1.312 and
MAPE = 9.715 show that this model is not capable of delivering exact level forecasts
in times of increased volatility. For Munich, I conclude that we can describe the period
from 1999 to 2003 as a bubble.
Graph 36: Long-Run Rent Model Forecast Outcomes – Munich
13
12
11
10
9
8
7
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nine-year
Munich
x Nuremberg:
The Nuremberg seven-year model, the best long-run model regarding RMSE and
MAPE (0.207 and 3.451 respectively), shows predictions that permanently lag behind
the actual rent level for one year. For example, both extrema are anticipated one year
too late and hence, the level is overestimated until 2004. Afterward, it is permanently
underestimated, as graph 37 indicates. Nevertheless, even this specification
demonstrates the major impact of economic fundamentals for the determination of the
actual rent. The starting point is chosen within the rent level upswing before reaching
the peak.
102
Graph 37: Long-Run Rent Model Forecast Outcomes – Nuremberg
7.6
7.2
6.8
6.4
6.0
5.6
5.2
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Seven-year
Nuremberg
x Stuttgart:
For Stuttgart, the chosen eight-year model also shows a deviation of the forecasts
from the actual values. In contrast to Nuremberg, this time the forecasts overestimate
one year in advance while the actual rent series increases and underestimate in the
drop phase as graph 38 illustrates. However, the extremum in 2002 are correctly
anticipated. The performance measures for this model are RMSE = 0.289 and MAPE =
3.492. The starting value is situated one year before the trough in 1999.
Graph 38: Long-Run Rent Model Forecast Outcomes – Stuttgart
11
10
9
8
7
6
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nine-year
Stuttgart
103
5.4.2. Conclusion
This single city analysis demonstrates that for the cities under study the demand proxy
"Office Employees" and the supply proxy "Office Space Inventory" with lag 1 are
sufficient indicators for determining the actual rent's long-run pattern. Thus, changes
in the economic fundamentals are the primer sources for the long-run development of
rents in these markets. In the long run, these markets seem to be rational. On the other
hand, actual rent level deviations from the economic fundamentals’ predictions are
short-run phenomena due to speculative factors or other market inefficiencies which
do not have long-run influence on the rent level. This was especially well
demonstrated with the example of Munich.
As illustrated in the preceding subchapter, for most cities the best performing
models based on fundamentals start the forecasts in more or less the same range:
between 1998 and 2001. Thus, the roughly similar starting points do not seem to be
random choices. The respective starting point for each of the cities is not situated in a
peak. For most of the cities, in order to recognize a rent level trough in the mid- or late
1990s and demonstrate a peak around 2001, the "optimal" starting point is a year when
the rent level is close to the trough or at the beginning of the upswing in the late 1990s,
thus at a time when markets are at moderate levels.
The chosen starting values represent city-specific rent values at times when they
are at economically reasonable levels. Thus, at these times the rent value is completely
or almost completely determined by its economic fundamentals and without the
significant influence of other variables. I argue that this is the case here, since, at least
for the period captured, the actual rent level after this point in time can be precisely
forecasted by a model based on the rent’s economic fundamentals.99
Hence, I derive the following rule for all starting values: They are positioned at a
point in time when rents are (almost) completely determined by the market forces of
demand and supply. Consequently, these points in time represent good starting values
for rent forecasts which intend to capture the long-run equilibrium rent. Short-run
phases of rent level increases or decreases that are not caused by economic
developments but are induced by, for instance, speculation or restricted market
mechanisms cannot be forecasted by this model.
99
Hott & Monnin (2008) give the same interpretation in reference to their findings.
104
In this long-run investigation, I used samples starting from 1992 and stopping
between 1997 and 2001. When I apply the total sample available from 1992 until 2006
to estimate the multivariate forecasting model, the coefficients are stable and thus in
the same range as in the smaller samples. Hence, starting the forecasts at the chosen
starting point shows a similar pattern for this in-sample forecast compared with the
out-of sample forecast.100 Realizing this, I make the assumption that this pattern - the
determination of the long-run rent development in the nine German office markets by
only one demand and one supply variable - is also valid for the future. This
conclusion, of course, implies further sub-assumptions, such as that the free market
price mechanism is not prevented from functioning by official authorities or disturbed
by market inefficiencies that last for the long run. Consequently, with forecasts of the
explanatory variables "Office Employees" and the "Office Space Inventory" up to the
desired forecasting horizon, these models, in combination with the respective starting
values, can be applied for even longer-term rent series out-of sample forecasts.
5.5. Chapter Conclusion
In this last subchapter of chapter 5 I analyze whether the research hypotheses
presented in chapter 4.1 can be accepted or whether they must be rejected.
x Research Hypothesis 1: Univariate models and multivariate models are not
appropriate to forecast rent series in the German office market.
Rejected: In general, the tested ARIMA, GARCH and multivariate regression models
are able to forecast rent series in the German office market. However, one has to
consider that the exogenous variables in the multivariate regression models have to be
forecasted as well before being implemented into the model to determine the forecasts
of the endogenous variable. This fact is a considerable source of increased forecasting
errors.
x Research Hypothesis 2: GARCH models do not help to outperform simple
ARIMA models in times of increased volatility.
Rejected (partly): For Frankfurt and Munich, cities showing increased volatility
throughout the time period examined, forecasts based on GARCH models are able to
100
Estimation and forecasting outputs are not depicted here, but are available upon request.
105
outperform those based on ARIMA models for forecasting horizons of three to five
years. In the shorter run, no improvement could be detected.
x Research Hypothesis 3: There are no economic or real estate variables that
significantly influence the development of the rent series.
Rejected: The variables studied, “Office Employees”, “Office space inventory”,
“Vacancy; Office space”, “Gross value added; Public & private services”, “Consumer
Price Index, Germany”, “Construction Price Index-new office buildings, Germany”,
“Germany Interbank 12 mth (LDN: BBA) - offered rate”, and “Germany (DEM) IR
Swap 10 Year - middle rate “, or their lag and first difference specifications, show
significant correlations with the first difference of the rent series. This is not the case
for the variable “Gross value added; Financial & other services”.
x Research Hypothesis 4: To construct a multivariate model which convincingly
performs in forecasting the rent series, a single demand and a single supply
proxy are not sufficient.
Rejected: The first differences of the series "Office Employees" and "Office Space
Inventory" with lag 1 are sufficient to build a multivariate model that generates
forecasts which perform convincingly well.
x Research Hypothesis 5: There are no cities where one model is permanently
superior regarding forecasting performance.
Rejected: The univariate model completely dominates the forecasting performance in
Essen and Nuremberg. In Munich this is true for all but one forecasting horizons. On
the other hand, the multivariate model is the best performing for all but one forecasting
horizon in Dusseldorf and Hamburg.
x Research Hypothesis 6: Univariate models do not result in superior forecasts
for rent series in major German cities, especially in the short run.
Rejected: According to the performance measures, univariate models outperform their
multivariate counterparts in about 70% of the cases with a forecasting horizon of one
to three years.
106
x Research Hypothesis 7: A multivariate single equation model with economic
explanatory variables does not produce superior forecasts, especially in the long
run.
Rejected: According to the performance measures, multivariate models outperform
their univariate counterparts in 75% of the cases with a forecasting horizon of five
years.
x Research Hypothesis 8: The long-run rent level is not mainly determined by its
economic fundamentals.
Rejected: According to the graphical analysis most cities’ actual rent can relatively
precisely be replicated by the predictions of the multivariate model applying economic
fundamentals. Thus, for these markets, changes in the economic fundamentals are the
prime sources for the long run development of rents.
x Research Hypothesis 9: Speculative factors play a role in the long-run
determination of the rent level.
Rejected: Actual rent level deviations from the economic fundamentals’ predictions
are short-run phenomena due to speculative factors or other market inefficiencies
which do not have long-run influence on the rent level. In the long run, only changes
in the economic fundamentals have explanatory power for the rent level development,
as can be seen by the graphs in chapter 5.4. For Munich this becomes particularly
clear.
x Research Hypothesis 10: A forecast starting value at a point in time when rents
are at an economically reasonable level is not crucial to precisely predicting the
rent level in the longer run.
Rejected: For no city is the respective forecast starting point for predicting precise
forecasts for the total horizon situated in a peak. For most of the cities, in order to
replicate a rent level trough in the mid- or late 1990s and demonstrate a peak around
2001, the "optimal" starting point is a year when the rent level is close to the trough or
in the beginning of the upswing in the late 1990s. The chosen starting values represent
city-specific rent values at times when they represent economically reasonable levels.
107
Thus, at these times, rent values are completely or almost completely determined by
their economic fundamentals and without the significant influence of other variables or
speculation.
108
6.
Empirical results: Total yield forecasting
This chapter examines the total yield, which is a return measure combining rental and
price yields.101 I proceed similar as in subchapter 5.1.1, 5.2 and 5.4 to simplify the
comparison with the rent model analysis. As can be noticed, I was only able to
undertake the multivariate examination, since the total yield series for the individual
cities are too short to run a univariate analysis. This also implies that only certain
hypotheses could be tested empirically for the total yield series.
Hence, I start the empirical work in this chapter by analyzing the total yield
series for city specifics, and I give interpretations by scrutinizing different influences
on the total yield in subchapter 6.1. In subchapter 6.2, I first present a correlation
analysis of total yield and different potentially influential variables. This is the basis
for the construction and estimation of multivariate total yield forecasting models,
whose forecasting results for each city for the one- to five-year forecasting horizons
are moreover presented eventually.102 The best fitting city-specific long-term total
yield forecasting models are delineated in subchapter 6.3. Subchapter 6.4 provides the
conclusion.
6.1. Total yield series analysis
In this subchapter I analyze each individual city's total yield series graphically and
give detailed interpretations. Furthermore, I briefly compare the outcomes with the
respective development of the rent and the price series. In the second part, I comment
on the general composition and characteristics of the series by illustrating influences of
the rent series as well as the price series development. Finally, I discuss the stationarity
of the combined series by interpreting the results of the applied panel unit root test.
6.1.1. Total yield data description
x Cologne:
The Cologne total yield series can be subdivided into three major phases. Phase
one presents a strong upswing in the series after a weak downturn in the 1990s. After a
101
102
For a more detailed definition refer to chapter 4.3.
Since the city-specific total yield series are too short, I have to reject the estimation of the
univariate models assessed for the rent forecasts in chapter 5.1.
109
peak of around 12% in the year 2000, the years until 2003 are characterized by a
strong reduction in the total yield, up to -2%, as indicated by graph 39. After 2003
another tremendous increase in the series can be observed, which rises to 12% in 2006.
In summary, the Cologne total yield development shows high volatility in the time
horizon examined. The peak in the year 2000 is, moreover, one year before the
comparable peak in the rent series, according to the analysis in chapter 5.1.1. The same
can be observed for the price series peak visible in graph 1 in the appendix. A further
difference to the rent development is the last phase with its high yield increase. This is,
however, already denoted in the price series.
Graph 39: Cologne Total Yield Series
.12
.10
.08
.06
.04
.02
.00
-.02
-.04
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Cologne
x Dusseldorf:
In Dusseldorf, as can be seen in graph 40, the total yield level represents a steady
development in a range between 5 to 9% until 2002. Afterward, in the period until
2005, the Dusseldorf total yield series plummets by as much as to -23% aside from an
interim peak in 2004. This formation can be explained by the general decrease in total
yield in 2003 and the recovery afterward, which can be observed in most of the other
major German office markets. However, the intervening crash in 2005 can only be
explained by a massive jump in the office space supply after 2004103 and the resultant
price crash in 2005.104 The last year of the part of the series analyzed again shows a
positive yield of 8%.
103
Figures regarding office space inventory change for Dusseldorf in the years mentioned are not
depicted here. However, they can be provided by the author upon request
104
For further information refer to graph 2 in the appendix.
110
Graph 40: Dusseldorf Total Yield Series
.12
.08
.04
.00
-.04
-.08
-.12
-.16
-.20
-.24
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Dusseldorf
The Dusseldorf total yield series is characterized by extreme volatility caused by
the extraordinarily negative development in the first years of the new millennium and
the enormous rebound in 2006. The pattern is comparable to the rent series as well as
the price series development.
x Essen:
Graph 41: Essen Total Yield Series
.16
.12
.08
.04
.00
-.04
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Essen
Examining graph 41, I determine two different phases for the total yield
development in Essen. The first period, until 2000, is characterized by a volatile
development, ranging from 1 to 15%. After 2000 there is a period with a steady
development. During this time, the total yield development is less volatile and at a
lower level, ranging between -1 and +5%. This evolution is similar to the rent series
111
and the price series formation, while the rent and especially the price level decrease to
a greater extent. This can be observed in graph 4 and graph 3 in the appendix.
x Frankfurt:
Graph 42: Frankfurt Total Yield Series
.3
.2
.1
.0
-.1
-.2
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Frankfurt
The Frankfurt total yield development can be subdivided into three different
phases. Until the year 2000, graph 42 shows a volatile increase of up to 25% in the
total yield. This is followed by a radical decline to -15% in 2003 and a rebound to
almost 9% in 2006. Similarly to Cologne, the peak in 2000 is one year before the
respective rent series and price series peak. Moreover, within the rent development,
there is no increase in the level during the last years of the period examined, as can be
observed in graph 5. This, however, is denoted by the price series.105
x Hamburg:
A similar pattern as in Frankfurt or Cologne can be discovered for the Hamburg
total yield series. After some years of steady development, there is a strong increase
from around 0% to 11% up to the year 2000. Until 2003 the total yield series drops
dramatically, with a trough of -12% in 2003. From 2003 to 2006 the series recovers to
around 5%. Again, the peak is one year earlier compared to the respective rent series
and price series. This time, the final upswing according to graph 43 cannot be seen the
price series development106, but is denoted in the rent series, as graph 6 illustrates.
105
For evidence refer to graph 4 in the appendix.
106
For evidence refer to graph 5 in the appendix.
112
However, the strong decrease in price level ends, and one can observe a slightly
relatively steady development.
Graph 43: Hamburg Total Yield Series
.15
.10
.05
.00
-.05
-.10
-.15
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Hamburg
x Leipzig:
Graph 44: Leipzig Total Yield Series
.15
.10
.05
.00
-.05
-.10
-.15
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Leipzig
The Leipzig total yield series between 1993 and 2006 can be subdivided into two
major parts. The first period, until 1996, is best described as a volatile phase, with a
final crash in 1996, in which the total yield drops from around 13% in 1995 to around 11%. Afterward, the series is characterized by an upswing with decreasing volatility,
reaching a total yield of almost 13% in 2006. This pattern is completely different from
the rent development, where there is a non-volatile steady development with a mild
113
decrease throughout the last years of the period, according to graph 7 in chapter 5.1.1.
The same is true for the price series development.107
x Munich:
Graph 45: Munich Total Yield Series
.4
.3
.2
.1
.0
-.1
-.2
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Munich
In Munich I identify three different sub-periods, as can be observed in graph 45.
The first years are characterized by a steady but strong increase in the total yield
series, from around -13% in 1994 up to + 30% in the year 2000. Subsequently, there is
a strong decrease to -9% in 2002 and finally -15% in 2004. A rebound to almost 0%
signifies the last phase. This pattern is comparable to Cologne, Frankfurt, and, to some
extent, Hamburg. With a peak in 2000, one year before the rent and prices series
peaks, the series presents an extreme drop, with a trough in 2004, which is one year
later, just as in the other cities. Furthermore, the yield recovery during the last years of
the period examined is not as strong, since the price is declining further, according to
graph 7 in the appendix.
x Nuremberg:
Nuremberg's total yield series shows a different pattern than any other city; it
manifests a double peak in the years 1998 and 2000. Before this volatile phase, there is
a steady development in the range of -1 to -4%. After the peak in 2000, there is a
strong decrease until 2002. Afterward, a steady rebound can be observed, according to
graph 46. For Nuremberg the time of the second peak is the same as the rent peak.
107
For evidence refer to graph 6 in the appendix.
114
However, the price series replicates the double peak completely, as can be seen in
graph 8 in the appendix. Furthermore, the upswing throughout the last years also takes
place within the rent series.
Graph 46: Nuremberg Total Yield Series
.16
.12
.08
.04
.00
-.04
-.08
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nuremberg
x Stuttgart:
Graph 47: Stuttgart Total Yield Series
.2
.1
.0
-.1
-.2
-.3
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Stuttgart
For Stuttgart I subdivide the total yield series into three major phases. The first is
characterized by an extreme drop of up to -26% in 1995. After the rebound in the
subsequent years, there is more or less a steady development from 0 to 10% until the
end of the observed time period, which only slightly presents the peak, trough, and
rebound constellation of the other examined cities. Compared to the rent series, the
interim peak in 2001 is one year too early. However, it is contemporaneous in the price
115
series, where an interim peak can be observed. The subsequent slight upswing is
replicated only by the rent series in 2006.
6.1.2. Interpretations and conclusions
According to this city analysis, I detect a general total yield pattern for Cologne,
Dusseldorf, Frankfurt, Hamburg, Munich, Nuremberg, and Stuttgart. Especially, the
series development of Cologne, Frankfurt, Hamburg, and Munich are very similar,108
with all of these cities experiencing a peak around the year 2000 and a trough around
the year 2003. Afterward, one can observe a total yield recovery.109 For most of the
cities this means differences from the rent and price series development. The peak is
more or less one year earlier as well as the trough.110 Thus, the total yield series can be
regarded as a forerunner of the rent and price series. Furthermore, the rebound in the
total yield series cannot, in general, be recognized in the rent development; however, it
can be observed in the price series. This hints at the importance of the price series in
determining the total yield. This fact is also underlined by the prominent double peak
in the Nuremberg total yield, which is only displayed by its price series.
According to the total yield definition,111 it becomes clear that the overwhelming
influence on the total yield must come from the price yield. This is illustrated by
graphs 10 to 18 in the appendix. Here, the rental yield is very constant over the years
due to the direct connection between rent and price without major lead or lag relation.
It only controls parts of the level of the total yield. One could say that the rental yield
puts a steady premium on the price yield. On the other hand, it has almost no influence
on direction. Thus, nearly all of the total yield volatility is based on the price
development.
108
Nuremberg, Dusseldorf and Stuttgart do not demonstrate the clear pattern of the other cities
mentioned. City-specific phenomena provide explanations for the deviations; however, they broadly
follow the same development.
109
Besides this similar pattern, one should be aware of the fact that the level as well as the
development amplitude is different throughout the cities.
110
This lagged pattern can be easily explained, since the sum of rental and price yield forms the total
yield. Both underlying series are only two relative expressions of the rent and the price series. Thus, an
extremum for the relative and the absolute series cannot be in the same year, since, for example, a
peak in the absolute series implies a gradient of zero. The peak in the relative series, however, is
situated at that point in time when the most positive gradient appears in the absolute series, and this
happens in our samples mostly in the year before the absolute extremum.
111
The total yield definition can be found in Definition 1 in chapter 4.3.2.
116
This major insight is also valid for Essen and Leipzig, the two cities that do not
show the same total yield pattern as the others. They seem to be somehow independent
from the other markets. Essen, on the one hand, shows an interim peak in 1999 and a
slight trough in 2003. However, the extent of these phenomena could also be attributed
to general volatility. The extrema are not as clearly shaped as in the other cities. Since
Essen, as a part of the Ruhr Area, had to deal with a high degree of transformation
from heavy industries to service industries throughout the last years of the period
examined, the special development of its office market's can be explained. On the
other hand, the Leipzig total yield series does not demonstrate any similarity with the
other cities; rather, it shows a steady increase throughout the last years of the
examined period. This increase can be attributed to a shrinking level of price decrease
which eventually leads to a slight price increase in 2006, according to graph 6 in the
appendix, combined with the steadily positive rental yield.112 The deviating behavior
of the Leipzig total yield development can be explained by the fact that Leipzig is
situated in the eastern, former communist, part of Germany. It also had to deal with
massive transformations of its industries and other societal changes. Especially in the
office market, Leipzig experienced enormous speculation directly after German
reunification in 1990, with a tremendous but steady downturn in the aftermath.
Concluding, with respect to total yield, most of the major German office markets
examined demonstrate a similar pattern, which hints at a broad investor market with
high interrelations between these cities. Only two cities were considered explainable
exceptions.
As a final step for this subchapter, I applied a panel unit root test to the combined
total yield series to test for stationarity. The results present a stationary level series.113
Thus, no first differencing of the total yield series has to be undertaken. Since the total
yield is the sum of the two relative series rental yield and price yield, and price yield is
nothing other than the log of the first difference of the price series, the finding of a
stationary series and thus no necessary transformation was to be expected.
112
For evidence please refer to graph 15 in the appendix.
113
For evidence please refer to table 19 in the appendix.
117
6.2. Multivariate models
Chapter 6.2 is organized as follows. I start with an examination of a range of possible
explanatory variables regarding stationarity. A correlation analysis is then conducted
between the stationary series of these variables and the total yield series. In chapter
6.2.2, single equation panel models for the different forecasting horizons are
estimated, and their outcomes are discussed briefly. Then the total yield series are
forecasted for each city using these models. Finally, the forecasting outcomes for the
one- to five-year models are presented and interpreted.
6.2.1. Explanatory variables analysis
Similarly to the procedure in the rent correlation analysis in chapter 5.2.1, I choose
indicators from different sources that general literature considers as proxies for office
space demand or supply or as generally influential on total yield in office markets.
Since they are the same as in the rent analysis, no further examination of stationarity
has to be undertaken.
With the first differences of the combined potential explanatory variables I now
conduct a correlation analysis with the total yield series. The results can be observed in
table 40.
Table 40: Correlation analysis: Total Yield vs. potential explanatory variables114
Total Yield
d(Office Employees)
d(Office space inventory) (-1)
d(Vacancy; Office space) (-1)
d(Gross value added; Public & private services)
d(Gross value added; Financial & other services)
d(Consumer Price Index, Germany) (-2)
d(Construction Price Index-new office buildings, Germany) (-3)
d(Germany Interbank 12 mth (LDN: BBA) - offered rate) (-1)
d(Germany (DEM) IR Swap 10 Year - middle rate) (-3)
0.4602*
-0.4001*
-0.4098*
0.2359*
-0.2160
-0.2365*
0.2721*
-0.3415*
The correlations between the total yield series and the first difference of the
potential explanatory variables are very similar to the outcomes of the rent correlation
analysis, as could be expected. However, there are some minor differences in the
114
The expression d(.) means that the expression within the brackets is first differenced.
118
magnitude of the relations. On the other hand, for two variables, I observe stronger
correlations for different lags than in the rent analysis.
The correlation between the first difference of "Office Employees" and the total
yield series is positive, as in the rent analysis, yet slightly stronger. As marked by the
asterisk in table 40, this correlation with a coefficient of 0.46 is significantly different
from zero on the 1% level. Again, this could be expected. As an example, a positive
change in "Office Employees" as a positive impulse from the demand side for office
space should lead to increasing rents ceteris paribus. As in the rent analysis, the
opposite relation can be observed for the correlation between the first difference of
"Office Space Inventories" with lag 1 as a supply impulse and the total yield series.
The significantly negative coefficient of around 0.4 is close to the displayed value in
chapter 5.2.1. Again, a clear causal relation can be detected, as expected. I found the
first major difference in this analysis compared to the rent examination when looking
at the correlation between the first difference of "Vacancy, Office Space" and the total
yield series. After testing for different lag constellations, the most significant
correlation is found when applying total yield and lag 1 of the first difference of
"Vacancy, Office Space". Although again the correlation between the explained and
the potential explanatory variable exists, also without lag, the negative coefficient of
around -0.4 implementing lag 1 is more influential. Again, I expected this negative
relation since "Vacancy, Office Space" is another proxy for office market supply. As
in the rent analysis, a positive correlation between the first difference of "Gross Value
Added; Public & Private Services" and the total yield series is detected. Here, the
coefficient of 0.24 is significantly different from zero on the 1% level. Nevertheless,
the comparably low coefficient value indicates small influence of this variable. Once
more, I suppose that this demand proxy is not specific enough for explaining rent level
changes. Just as in the rent analysis, the first difference of "Gross Value Added;
Financial and other Services" has no explanatory power for total yields independent of
the chosen lag structure. Furthermore, the first differences of both chosen price
indicators do show negative correlation coefficients. The correlation between the first
difference of "Consumer Price Index, Germany" with a chosen lag 2 and the total yield
series is -0.2, which is a mirror of the rent examination outcomes. However, I
determined that this correlation is significant even on the 1% level. On the other hand,
the correlation of the first difference "Construction Price Index-new office buildings,
Germany" series and total yield is most significant on a chosen lag 3, which means one
lag more than within the rent analysis. Finally, the two different interest rates were
tested regarding their influence on the total yield. Again, there is a positive correlation
119
between the first difference of "Germany Interbank 12 mth (LDN: BBA) - offered
rate" with a chosen lag of 1 and total yield, displaying a clearly positive coefficient of
around 0.3 and significantly different from zero on the 1% level. Moreover, there is a
negative correlation between the first difference of "Germany (DEM) IR Swap 10
Year - middle rate" with lag 3 and the total yield series. It is highly significant with a
correlation coefficient of -0.34. This outcome is also very close to the observed value
in the rent analysis.
6.2.2. Model construction and estimation
To construct the best performing total yield forecasting models for the different time
horizons, I employed a similar procedure to that of chapter 5.2.2 when building the
rent forecasting models. Again, I started with an implementation of the first
differences of the variables "Office Employees" and "Office Space Inventories" with
lag 1 as explanatory variables. Since both series are highly correlated with the total
yield series, I considered these demand and supply proxies as a good starting point for
constructing the models. In a second step, as in chapter 5.2.2, I compared the
performance of this basic model with models over all time periods that are enriched
with other influential indicators according to the total yield correlation analysis. Again,
none of these combinations achieves a significant improvement of the adjusted R² and
the applied performance measures. Moreover, many of these series do not show
significant influence on the dependent variable when implemented in the model.115
Their inclusion sometimes even affected spurious outcomes caused by
multicollinearity.
Ultimately, the best forecasting models for the different time horizons are in each
case the parsimonious models applying only the first differences of "Office
Employees", "Office Space Inventories"116. This result is stated according to the
applied performance measures and the adjusted R², which equals 0.55. Concluding, the
combination of only one demand variable and one supply variable is sufficient to
115
This finding was also recognized when lag 1 of the first difference of the vacancy rate was included
in the equation. According to my correlation analysis and seminal literature, the vacancy rate should
have played an important role. However, in my study it does not deliver an improvement in the
performance measures. On the other hand, for some applied samples this variable's coefficients display
values insignificantly different from zero.
116
Lag 1 of "Office space inventories" is employed according to the correlation analysis. Furthermore,
due to first order autocorrelation - determined by the Durbin-Watson statistics - this estimation was
corrected according to the Cochrane & Orcutt (1949) procedure.
120
forecast well the respective total yield within the nine German office markets included
in this investigation.117 All of the included panel series have the starting value 1992.
As in the rent analysis, the coefficients of the two independent variables are in
clear ranges within the different models. As expected, the coefficients of "Office
Employees" are always significantly positive and situated between 2.4 and 2.6, which
is significantly higher than in the rent models. The coefficients of lag 1 of "Office
Space Inventories", on the other hand, are always negative and significantly different
from zero. Here, the range is between -0.9 to -0.6. These results are depicted in table
20 in the appendix.
6.2.3. Discussion of the city total yield series forecasts
x Cologne
Table 41 displays the one- up to the five-year forecasts of the multivariate
forecasting model for the Cologne total yield series. The one-year forecast correctly
anticipates the positive total yield and, furthermore, presents the continued upward
development in total yield for 2006. However, the exact level is clearly
underestimated. The pattern for the two-year model forecasts is similar. On the one
hand, there is the correct prediction of positive total yields for both years. On the other
hand, the steady increase of the total yield level is observable. The total yield of 3.22%
in 2005 is exactly anticipated, whereas the 2006 value is again underestimated. In the
three-year forecasting horizon, one can see the same pattern for the yield predictions in
2005 and 2006. Conversely, the prediction for year 2004, the first year of the
forecasting horizon, is misleading. After the actual trough and extremum of the total
yield series with a value of -2.57% is positioned in 2003, the model predicts the trough
for 2004 continuing the downward development of the yield series, as table 41 shows.
Due to this underestimation, the levels for the two following years are also anticipated
too low. This one-year delayed prediction of the extremum and the subsequent too low
anticipation of the levels for 2005 and 2006 can also be observed in the four- as well
as the five-year model. Both models correctly result into negative yields for 2003,
where the five-year model gives an outcome that is very close to the actual figure. One
can also see these patterns in graph 48.
117
A test for panel cointegration demonstrated that the hypothesis of a cointegrated relation between
the series must be rejected. Thus, no Error Correction Model is applied. The employed multivariate
models are single equation panel models in their first difference representation.
121
Table 41: Multivariate Regression Total Yield Model Forecast Outcomes – Cologne
1998
1999
2000
2001
2002
2003
2004
2005
2006
Cologne
One-year
Two-year
Three-year
Four-year
Five-year
8.84%
10.33%
11.72%
10.34%
2.74%
-2.57%
2.99%
3.22%
11.49%
8.84%
10.33%
11.72%
10.34%
2.74%
-2.57%
2.99%
3.22%
4.44%
8.84%
10.33%
11.72%
10.34%
2.74%
-2.57%
2.99%
3.22%
4.02%
8.84%
10.33%
11.72%
10.34%
2.74%
-2.57%
-5.59%
0.22%
2.47%
8.84%
10.33%
11.72%
10.34%
2.74%
-4.70%
-5.90%
0.23%
2.57%
8.84%
10.33%
11.72%
10.34%
6.98%
-2.63%
-4.88%
0.81%
3.19%
Graph 48: Multivariate Regression Total Yield Model Forecast Outcomes – Cologne
.12
.12
.08
.08
.04
.04
.00
.00
-.04
-.04
-.08
-.08
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Cologne
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Cologne
x Dusseldorf
The Dusseldorf one-year forecasting model slightly underestimates the level of
the actual total yield in 2006. Nevertheless, the extremum in 2005 is anticipated
correctly and the prediction is very accurate compared to the high volatility in the
Dusseldorf total yield series after 2002. The two-year model correctly anticipates the
negative total yield in 2005 and the positive yield in 2006, thereby overestimating the
2005 level. It properly predicts both extrema in 2004 and 2005. The three-year model
displays the same pattern as the two-year model, with similar outcomes for 2005 and
2006. However, the extremum in 2003 is not anticipated. Therefore, a negative total
yield is shown instead of a positive value close to zero. The actual increase in total
yield in 2004 can also not be found by looking at the outcomes of the four- and the
122
five-year models. Nevertheless, these two models show accurate predictions for all
other years, including correct anticipation of the sign and the direction of the
development, as can also be observed in graph 49.
Table 42: Multivariate Regression Total Yield Model Forecast Outcomes – Dusseldorf
1998
1999
2000
2001
2002
2003
2004
2005
2006
Dusseldorf
One-year
Two-year
Three-year
Four-year
Five-year
6.80%
9.07%
9.02%
7.81%
5.85%
-2.67%
0.22%
-23.21%
8.17%
6.80%
9.07%
9.02%
7.81%
5.85%
-2.67%
0.22%
-23.21%
6.13%
6.80%
9.07%
9.02%
7.81%
5.85%
-2.67%
0.22%
-14.39%
6.59%
6.80%
9.07%
9.02%
7.81%
5.85%
-2.67%
-5.02%
-12.46%
5.67%
6.80%
9.07%
9.02%
7.81%
5.85%
-3.08%
-4.86%
-12.08%
5.70%
6.80%
9.07%
9.02%
7.81%
3.12%
-3.36%
-4.48%
-13.93%
6.09%
Graph 49: Multivariate Regression Total Yield Model Forecast Outcomes – Dusseldorf
.12
.12
.08
.08
.04
.04
.00
.00
-.04
-.04
-.08
-.08
-.12
-.12
-.16
-.16
-.20
-.20
-.24
-.24
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Dusseldorf
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Dusseldorf
x Essen
All different time horizon models perform relatively poorly for Essen, which
could be expected, considering the results of the rent series analysis. According to
table 43, the one-year model correctly anticipates a positive total yield. However, the
model does not cover the local extremum in 2005, thus presenting a value that is too
low in 2006. The same pattern can be detected for the two-year model with a very
accurate prediction for 2005. The extremum in 2003 is not anticipated by the three-,
the four-, or the five-year model. Instead of displaying a negative value, the four- and
123
the five-year models show positive yields followed by incorrect negative values for all
three models in 2004. All three models appropriately forecast positive total yields for
the years 2005 and 2006; however, the values underestimate the actual numbers.
Furthermore, the five-year model does not show the upturn in total yield in 2002, thus
predicting a too low value, as can be seen in graph 50. Concluding, in Essen there are
more influences that determine the total yield than just the change in economic
demand and supply fundamentals.
Table 43: Multivariate Regression Total Yield Model Forecast Outcomes – Essen
1998
1999
2000
2001
2002
2003
2004
2005
2006
Essen
One-year
Two-year
Three-year
Four-year
Five-year
1.24%
12.16%
1.34%
0.67%
3.86%
-1.24%
4.48%
3.97%
5.00%
1.24%
12.16%
1.34%
0.67%
3.86%
-1.24%
4.48%
3.97%
2.35%
1.24%
12.16%
1.34%
0.67%
3.86%
-1.24%
4.48%
4.07%
2.13%
1.24%
12.16%
1.34%
0.67%
3.86%
-1.24%
-4.37%
0.73%
0.46%
1.24%
12.16%
1.34%
0.67%
3.86%
1.37%
-3.31%
1.14%
0.74%
1.24%
12.16%
1.34%
0.67%
0.49%
0.73%
-2.74%
1.75%
1.39%
Graph 50: Multivariate Regression Total Yield Model Forecast Outcomes – Essen
.16
.16
.12
.12
.08
.08
.04
.04
.00
.00
-.04
-.08
-.04
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Essen
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Essen
x Frankfurt
With respect to table 44, the models are work well in forecasting the total yields
for the Frankfurt market regarding direction and algebraic sign. Nevertheless, the
level, especially in the years with high amplitude, is forecasted more conservatively,
124
that is, closer to zero than the actual outcomes show. This is all true for the one- and
the two-year models. The three-year model correctly anticipates the trough in 2003,
forecasting the upward direction of the total yield series in the aftermath. However,
while the actual outcome in 2004 is accurately predicted, the levels in 2005 and 2006
are predicted too low, showing even a negative value for 2005. For the four- and the
five-year model, the general patterns detected are valid. Thus, they correctly predict
the algebraic signs for the respective horizons, with the only exception being the first
year in the five-year model. Furthermore, the direction and thus the extrema are exact,
with too low amplitude regarding the forecasted total yield levels. This is underlined
by graph 51. It seems that the Frankfurt market tends toward exaggerations in the
direction of both sides in the forecasting horizons examined for the total yield series.
Table 44: Multivariate Regression Total Yield Model Forecast Outcomes – Frankfurt
1998
1999
2000
2001
2002
2003
2004
2005
2006
Frankfurt
One-year
Two-year
Three-year
Four-year
Five-year
4.71%
24.34%
25.64%
13.94%
-1.84%
-15.00%
-8.14%
4.28%
8.69%
4.71%
24.34%
25.64%
13.94%
-1.84%
-15.00%
-8.14%
4.28%
5.11%
4.71%
24.34%
25.64%
13.94%
-1.84%
-15.00%
-8.14%
0.18%
3.53%
4.71%
24.34%
25.64%
13.94%
-1.84%
-15.00%
-8.48%
-0.40%
2.88%
4.71%
24.34%
25.64%
13.94%
-1.84%
-7.01%
-5.82%
0.49%
3.21%
4.71%
24.34%
25.64%
13.94%
2.03%
-5.13%
-4.71%
1.23%
3.82%
Graph 51: Multivariate Regression Total Yield Model Forecast Outcomes – Frankfurt
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Frankfurt
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Frankfurt
125
x Hamburg
Table 45: Multivariate Regression Total Yield Model Forecast Outcomes – Hamburg
1998
1999
2000
2001
2002
2003
2004
2005
2006
Hamburg
One-year
Two-year
Three-year
Four-year
Five-year
-0.63%
10.22%
11.38%
7.30%
1.26%
-12.28%
-1.58%
4.33%
5.76%
-0.63%
10.22%
11.38%
7.30%
1.26%
-12.28%
-1.58%
4.33%
8.66%
-0.63%
10.22%
11.38%
7.30%
1.26%
-12.28%
-1.58%
4.11%
8.32%
-0.63%
10.22%
11.38%
7.30%
1.26%
-12.28%
-3.11%
3.20%
7.77%
-0.63%
10.22%
11.38%
7.30%
1.26%
-3.38%
-0.34%
4.05%
7.97%
-0.63%
10.22%
11.38%
7.30%
0.25%
-3.07%
0.17%
4.58%
8.38%
Graph 52: Multivariate Regression Total Yield Model Forecast Outcomes – Hamburg
.15
.15
.10
.10
.05
.05
.00
.00
-.05
-.05
-.10
-.10
-.15
-.15
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Hamburg
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Hamburg
For Hamburg the total yield models also work very well. The one-year model
shows the right sign and the right direction, only exaggerating the level by about 3%.
The same is true for the two-year model, where, furthermore, the one-year forecast
matches the actual outcome almost perfectly. The three-year model delivers another
precise forecast by correctly anticipating the extremum in 2003 and displaying total
yield forecasts with the proper algebraic signs and the right upward direction. The
four-year model demonstrates a very similar pattern. Moreover, it is certainly
remarkable that the trough in 2003 is predicted, but its total extent is not completely
covered, as graph 52 illustrates. A very close result can be observed for the five-year
model.
126
x Leipzig
Table 46: Multivariate Regression Total Yield Model Forecast Outcomes – Leipzig
1998
1999
2000
2001
2002
2003
2004
2005
2006
Leipzig
One-year
Two-year
Three-year
Four-year
Five-year
-0.65%
3.79%
-3.51%
6.12%
0.92%
7.94%
8.06%
8.75%
12.74%
-0.65%
3.79%
-3.51%
6.12%
0.92%
7.94%
8.06%
8.75%
9.95%
-0.65%
3.79%
-3.51%
6.12%
0.92%
7.94%
8.06%
3.31%
7.92%
-0.65%
3.79%
-3.51%
6.12%
0.92%
7.94%
1.50%
0.55%
6.76%
-0.65%
3.79%
-3.51%
6.12%
0.92%
2.35%
0.05%
0.29%
6.63%
-0.65%
3.79%
-3.51%
6.12%
2.15%
3.19%
0.89%
1.04%
7.12%
.
Graph 53: Multivariate Regression Total Yield Model Forecast Outcomes – Leipzig
.15
.15
.10
.10
.05
.05
.00
.00
-.05
-.05
-.10
-.10
-.15
-.15
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Leipzig
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Leipzig
The models correctly forecast the positive total yields for Leipzig in the one- up
to the five-year horizons. However, they only partly show proper anticipation of the
extrema and thus poor level predictions. The one-year model delivers a good result by
slightly underestimating the true outcome of the total yield, thereby showing the right
sign and direction. The two-year model predicts an extremum in 2004 and in 2005.
However, considering the actual values, there is no such kink. Thus, the 2005 and
2006 values are underestimated. In the three-year model the peak is anticipated in
2003, and the 2005 trough remains the same. Thus, the values for the total horizon are
also underestimated. The same pattern as for the three-year forecasting model is true
for the four-year model, but the actual total yield increase in 2003 is clearly
underestimated. The same picture is also given by the five-year model, as graph 53
127
shows. Here, the two actual extrema in 2001 and 2002 are correctly anticipated. This
analysis underlines that the development of the economic fundamentals does have
influence on the total yield for Leipzig. However, there seem to be other influences
x Munich
Table 47: Multivariate Regression Total Yield Model Forecast Outcomes – Munich
1998
1999
2000
2001
2002
2003
2004
2005
2006
Munich
One-year
Two-year
Three-year
Four-year
Five-year
3.48%
12.46%
30.45%
19.69%
-8.90%
-10.93%
-15.45%
-1.33%
-0.58%
3.48%
12.46%
30.45%
19.69%
-8.90%
-10.93%
-15.45%
-1.33%
1.25%
3.48%
12.46%
30.45%
19.69%
-8.90%
-10.93%
-15.45%
1.72%
1.92%
3.48%
12.46%
30.45%
19.69%
-8.90%
-10.93%
-6.15%
4.25%
2.08%
3.48%
12.46%
30.45%
19.69%
-8.90%
-9.84%
-5.55%
4.41%
2.27%
3.48%
12.46%
30.45%
19.69%
5.04%
-5.09%
-3.81%
5.27%
3.01%
The Munich one-year total yield forecasting model correctly presents a value that
has increased since the year before. However, the predicted outcome, which is
supposed to be slightly negative, turns out to be positive. The same is true for the twoyear model, where both values should be negative but turn out to be positive.
However, the direction is, once more, correct, and considering the high volatility in
total yields at these times,118 the actual values are anticipated very precisely. The
trough in 2004 is wrongly predicted for 2003 by the three- to five-year models. Even
though the forecasted values for 2004 are strongly negative, they do not meet the
actual amplitude, and the models predict an even more negative value for 2003. For
2005 the three- to five-year models have a value overshoot in common, showing a
clearly positive number where a negative yield was expected. A rebound in the
forecasted values to the actual yields can then be observed for the 2006 predictions, as
graph 54 shows. Moreover, the five-year model anticipates to a great extent the crash
in total yield values caused by the Munich office building price collapse after 2001.
118
Total yields deviate from -15% to -1% in one year as can be observed in table 47.
128
Graph 54: Multivariate Regression Total Yield Model Forecast Outcomes – Munich
.4
.4
.3
.3
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Three-year
Munich
Four-year
Five-year
Munich
x Nuremberg
Table 48: Multivariate Regression Total Yield Model Forecast Outcomes – Nuremberg
1998
1999
2000
2001
2002
2003
2004
2005
2006
Nuremberg
One-year
Two-year
Three-year
Four-year
Five-year
14.92%
2.76%
15.00%
5.29%
0.33%
2.70%
4.88%
7.54%
10.20%
14.92%
2.76%
15.00%
5.29%
0.33%
2.70%
4.88%
7.54%
8.47%
14.92%
2.76%
15.00%
5.29%
0.33%
2.70%
4.88%
5.38%
7.54%
14.92%
2.76%
15.00%
5.29%
0.33%
2.70%
1.51%
4.11%
6.81%
14.92%
2.76%
15.00%
5.29%
0.33%
-3.05%
-0.05%
3.69%
6.68%
14.92%
2.76%
15.00%
5.29%
0.21%
-2.41%
0.58%
4.08%
7.06%
The Nuremberg forecast values almost completely underestimate the actual total
yield outcomes. As illustrated in graph 55, one could almost speak of a parallel
translation. Since algebraic sign and direction are correct and the level is only slightly
underestimated by the one- and the two-year models, the above-mentioned pattern
visibly appears for the three- to five-year models, thereby setting the trough in 2004
for the three-year model and in 2003 for the four- and five-year models respectively.
The actual trough, however, is in 2002. Thus, for Nuremberg the economic
fundamentals do explain the direction of the yield, yet with one to two years delay. I
interpret this as a kind of permanent premium within the market in the time period
examined.
129
Graph 55: Multivariate Regression Total Yield Model Forecast Outcomes – Nuremberg
.16
.16
.12
.12
.08
.08
.04
.04
.00
.00
-.04
-.04
-.08
-.08
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Three-year
Nuremberg
Four-year
Five-year
Nuremberg
x Stuttgart
Table 49: Multivariate Regression Total Yield Model Forecast Outcomes – Stuttgart
1998
1999
2000
2001
2002
2003
2004
2005
2006
Stuttgart
One-year
Two-year
Three-year
Four-year
Five-year
-4.24%
-1.07%
5.09%
10.78%
4.27%
-0.64%
5.42%
3.51%
4.99%
-4.24%
-1.07%
5.09%
10.78%
4.27%
-0.64%
5.42%
3.51%
3.03%
-4.24%
-1.07%
5.09%
10.78%
4.27%
-0.64%
5.42%
6.53%
3.48%
-4.24%
-1.07%
5.09%
10.78%
4.27%
-0.64%
-2.81%
3.56%
1.77%
-4.24%
-1.07%
5.09%
10.78%
4.27%
-1.07%
-2.68%
3.62%
1.94%
-4.24%
-1.07%
5.09%
10.78%
7.30%
0.18%
-1.70%
4.24%
2.68%
Whereas the longer-run models show good predictions of Stuttgart's total yield in
2002 and 2003, the forecasts after 2003 are partly misleading. Since the models predict
the trough of 2003 for 2004, a development appears in this year that is supposed to go
in the opposite direction. However, for the three- to five-year models, the value for
2005, again, is precisely anticipated. This is not true for the two-year model, where we
can observe an overestimation of the year's total yield according to graph 56. All five
models underestimate the actual value for 2006; nevertheless, the positive total yields
in 2005 and 2006 are correctly anticipated.
130
Graph 56: Multivariate Regression Total Yield Model Forecast Outcomes – Stuttgart
.2
.2
.1
.1
.0
.0
-.1
-.1
-.2
-.2
-.3
-.3
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
One-year
Two-year
Three-year
Stuttgart
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Four-year
Five-year
Stuttgart
6.2.4. Conclusion
Subchapter 6.2 applied multivariate models to precisely forecast the total yield
development of nine German office markets. After a correlation analysis of the panel
total yield series with the first differences of several potential explanatory panel
variables, it turned out that the construction of a parsimonious model with a single
demand and a single supply variable as explanatory variables is sufficient to produce
good forecasting results in the time period examined. This was the case for the rent
model construction. Again, these included variables are the first differences of the
panel data series "Office Employees" and "Office Space Inventories". Similarly to the
rent models, these models can explain, on average, more than half of the variance of
the first differenced panel total yield series on average according to an adjusted R²
around 55%.
As concluded for the rent models, the general finding for the nine German office
markets analyzed is the major determination of the explained variable, here, the total
yield, by the market's economic fundamentals. There exists a clear relation between
the actual total yield and the development of "Office Employees" as a demand variable
and the development of "Office Space Inventories" as a supply variable.119 Extrema,
and thus peaks and troughs, the direction of the development as well as the algebraic
signs of the total yields are forecasted correctly most of the time. Nevertheless, the
119
However, this is not the whole truth for the exceptions Essen and Leipzig, since both cities’ actual
total yield development deviates from the forecasts and thus reveals further influences in determining
the cities’ total yield that are not included in the multivariate panel regression model.
131
amplitude of the total yields is often different from the actual outcomes. This can be
attributed to the high actual total yield volatility in the series within the observed time
horizon. Another technical difference is that, for cities with poor rent level predictions
in the four- or five-year forecasting horizons, the respective total yield outcomes show
much better performance. A discussion of the reasons is given at the end of chapter
6.3.
6.3. Long-run forecasting models
This subchapter presents and examines multivariate forecasting models for each city
that are able to capture the respective long-run total yield pattern best. Here, the same
variables are chosen as for the multivariate regression models in the shorter run. The
only difference is the increased forecasting horizon and thus the reduced estimation
sample, whose exact size only depends on the respective city's forecasting starting
value.
To generate these models, each city is analyzed individually in the first
subchapter. There I present the model whose forecasts show the best performance
measures compared to other long-run forecasting models. The forecasting results are
shown graphically in comparison to the actual total yield series, and they are
interpreted with the support of the performance measure RMSE.120
6.3.1. Determination and interpretation
x Cologne
The seven-year forecasting model offers the most precise long-run total yield
predictions for Cologne. As can be observed in graph 57, the forecasted values follow
the actual total yield series very closely, at least until 2003. Afterward, one can
observe a parallel shift to the right. After not capturing the extremum in 2003, the
forecasted yield series does not match the actual series anymore. However, after 2004
the direction as well as the algebraic sign of the forecasts is correct. Thus, I argue that
the Cologne total yield series follows its economic fundamentals in the longer run. The
starting point chosen for the model is 1999, where the series is situated in an upswing,
120
Since the total yield series is a percentage measure, RMSE is also presented in percentage. Thus, I
reject the application of MAPE.
132
but not yet at the peak. This is the same pattern as with the rent series. It is only shifted
back one year since the total yield series peaks one year earlier. Furthermore, an
RMSE of 0.047 in this seven-year forecast is considerably lower than its average
counterparts of the one- to five-year models.
Graph 57: Long-Run Total Yield Model Forecast Outcomes – Cologne
.16
.12
.08
.04
.00
-.04
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Seven-year
Cologne
x Dusseldorf
Graph 58: Long-Run Total Yield Model Forecast Outcomes – Dusseldorf
.2
.1
.0
-.1
-.2
-.3
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Seven-year
Dusseldorf
For Dusseldorf, regarding the applied performance measures, the seven-year outof sample forecasting model offers the most precise predictions for the actual total
yield development.121 The outcomes very closely replicate the actual pattern in the
long run and show correct sign and direction most of the time. However, the interim
121
Here, the RMSE is 0.060.
133
peak in 2004 is not anticipated and the amplitude of the 2005 trough is clearly
underestimated.
Regardless, according to graph 58 it becomes clear that total yields in Dusseldorf
are mainly determined by demand and supply factors in the long run. In the year of the
starting point, 1999, the total yield is in a steady state. Considering graph 31 in chapter
5.4.1, the long-term rent model starts in 1997, which is also in the state of the series'
steady development.
x Essen
Graph 59: Long-Run Total Yield Model Forecast Outcomes – Essen
.16
.12
.08
.04
.00
-.04
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Eight-year
SER27
For Essen the eight-year out-of sample total yield forecasting model is chosen
because it delivers the best performance measures compared with the other tested
models.122 Here, the same starting value is chosen as for the rent model; however, the
model does not seem to perform well. According to graph 59, the forecasted pattern
appears to be one-year delayed compared to the actual outcomes. Thus, for the
determination of the total yield in Essen, the economic fundamentals also play a major
role. Yet, it seems as if the market participants anticipate and price in the development
of the economic fundamentals at least one year in advance. Taking that into
consideration and shifting back the forecasted yields by one year, extrema and signs
are replicated well. The same would be true for the level except during the last three
years. As already mentioned in the interpretation of the shorter run Essen total yield
forecasting models, at least for the year 2004, there seem to be other influences beyond
the economic ones.
122
For this model the RMSE is 0.059.
134
x Frankfurt
Graph 60: Long-Run Total Yield Model Forecast Outcomes – Frankfurt
.3
.2
.1
.0
-.1
-.2
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nine-year
Frankfurt
The Frankfurt nine-year total yield forecasting model replicates the actual
outcomes in the chosen time frame very precisely. The model's starting value is set in
1997, as in the rent model.123 Again, this is not a point in time when the series is at a
peak. Even though the model fails to anticipate the tremendous height of the total
yields around the millennium and provides forecasts a bit higher than the actual
outcomes in the following years, the pattern and thus the direction of the total yield
development are captured closely. Again, as observable in the four- and five-year
models, market exaggerations towards both sides compared to the fundamentals
become obvious.
x Hamburg
The Hamburg nine-year forecasting model generates very precise forecasts.124
The model exactly matches the extrema in 2000 and 2003, but the values in these years
are forecasted a bit too high, as can be seen in graph 61. In those years of extreme
prices, it seems that the market sets a negative premium on the fundamental prices.
Nevertheless, the algebraic signs are correct except for 2002. Hence, I conclude that
the total yield in Hamburg is determined by its economic fundamentals to a great
extent in the long run. The starting point is set in 1997, as in the rent model, and
123
The nine-year forecasting model has the best RMSE, 0.057.
124
Here, the RMSE is 0.030.
135
represents a year in an interim trough before the tremendous upswing in total yields
with its peak in 2000.
Graph 61: Long-Run Total Yield Model Forecast Outcomes – Hamburg
.15
.10
.05
.00
-.05
-.10
-.15
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nine-year
Hamburg
x Leipzig
Graph 62: Long-Run Total Yield Model Forecast Outcomes – Leipzig
.15
.10
.05
.00
-.05
-.10
-.15
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Seven-year
Leipzig
For the Leipzig total yield forecasting model, 1999 is set as a starting point due
to the comparably best RMSE of 0.062. This year is the same starting year as in the
long-term rent model, and it is situated at the top of an interim peak. Just as the
shorter-term forecasting models do, the seven-year model generates only positive
outcomes of the total yield, which is correct except for the year 2000. However,
especially during the first years of the chosen forecasting period, extrema as well as
levels are not predicted correctly. Only throughout the last years examined, is an
adjustment of the actual and the forecasted level values adumbrated. Thus, also for
Leipzig, economic fundamentals do have influence on the total yield development.
136
However, there are clearly other influences, at least during the first years of the
forecasting horizon chosen.
x Munich
For Munich a nine-year model was chosen to predict the development of the total
yields for the longer term. Thus, the model's starting value is set in 1997, as in the rent
model. This means a point in time before the tremendous total yield upswing in the
late 1990s with its peak in 2000. The model demonstrates that the economic
fundamentals determine the actual yield series of the city to a great extent, as can be
observed in graph 63. Furthermore, the performance measure RMSE = 6.2% displays a
better outcome than the comparable rent MAPE measure = 9.72%, underlining that the
detected rent bubble is very much offset by the extraordinarily high prices at the same
time. Thus, there is no bubble in the Munich market with respect to total yields.
Graph 63: Long-Run Total Yield Model Forecast Outcomes – Munich
.4
.3
.2
.1
.0
-.1
-.2
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nine-year
Munich
x Nuremberg
The Nuremberg seven-year model, the best long-run model regarding RMSE125,
shows almost the same pattern after 2002 as the shorter run models. Again, after
wrongly anticipating the extremum in 2003 and setting this trough in 2004, some kind
of premium or a lagging behind of the forecasts appears which only slowly diminishes
throughout the last years of the forecasting horizon. Nevertheless, the model works
well for the forecasted values throughout the first years, anticipating algebraic signs,
extrema and levels correctly. The only exception is the year 2000, where the total yield
peak is predicted too low. It seems that during that year a slight exaggeration - a mini
125
For this model the RMSE is 0.031.
137
bubble - was in the market. Again, the starting year is the same as in the rent model
and again not situated at a peak but in an interim trough. It can be concluded that the
economic fundamentals play a major role for the determination of the Nuremberg total
yield, and precise long-term forecasts are possible.
Graph 64: Long-Run Total Yield Model Forecast Outcomes – Nuremberg
.16
.12
.08
.04
.00
-.04
-.08
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Seven-year
Nuremberg
x Stuttgart
Graph 65: Long-Run Total Yield Model Forecast Outcomes – Stuttgart
.2
.1
.0
-.1
-.2
-.3
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Eight-year
Stuttgart
According to the best performance measure, I chose an eight-year forecasting
model for Stuttgart.126 The starting year, 1999, is the same as for the rent model and
situated at the beginning of an upswing in the series. This long-term model shows the
same pattern in the last years of the forecasting horizon as the shorter-term models do.
Again, the model predicts the trough of 2003 for 2004, including the kink in the latter
126
The eight year forecasting model for Stuttgart has a RMSE of 0.038.
138
year, which is supposed to appear in the opposite direction. Yet again, the value for
2005 is precisely anticipated, according to graph 65. During the first years the pattern
of the forecasted values is more similar to the actual outcomes, although, again, there
is a wrong specification of the extremum in 2001. This peak in total yield is placed in
2000 and hence one year too early. Concluding, for Stuttgart there seem to be other
influences; however, the economic fundamentals do play a major role in the
determination of the actual total yield.
6.3.2. Conclusion
This long-run single city examination illustrates for most cities under study that the
demand proxy "Office Employees" and the supply proxy "Office Space Inventory"
with lag 1 are sufficient indicators to determine the long-run total yield pattern in the
German office market.127 Directions as well as algebraic signs are mostly well
anticipated. Only some level predictions fail to be very precise, but again, as in the rent
analysis, these markets seem to be rational and thus ruled by economic fundamentals
as prime sources of the long-run total yield development. Compared to the rent
examination, the performance improvement of long-run models relative to their shortrun counterparts is not extraordinarily high. The reason is not that the total yield longrun models are much weaker regarding performance than the respective rent models.
In fact, the forecasts of the short-run models are already less biased, especially for
cities with high rent deviations.128 This is the case since the explained variable is
presented in percentage, which is different from the rent analysis, where the dependent
variable is shown in absolute values. In the latter case, the influence of an incorrect
forecast for an early year has a larger influence on the forecasting values in subsequent
years, since the biased absolute value is directly used as a base for the further
forecasts.129 Thus, for the total yield analysis a good starting value becomes less
important compared to the rent examination. As could be observed, there are not such
enormous deviations in, for example, the Munich total yield series.
127
Exceptions are Essen and Leipzig.
128
I found evidence of this in chapter 6.2.3, where I referred to the much better four- and five-year
total yield model forecasting performances in cities such as Frankfurt and Munich compared to the
respective rent model forecasting performances.
129
This is not the case for the total yield examination, since here the influence of a possibly biased
year affects the later years only through the AR(1) correction term. However, the forecasted value is
not directly used as a basis for the further years' forecasting values.
139
However, this does not mean that the starting value becomes irrelevant. For most
cities the best performing models based on fundamentals start the forecasts in more or
less the same range: between 1998 and 2001. Thus, the roughly similar starting points
do not seem to be random choices. For no city is the respective starting point situated
in a peak. For most of the cities retracing a total yield series trough in the mid- or late
1990s and demonstrating a peak around 2000, the "optimal" starting point is a year
when the total yield level is close to the trough or at the beginning of the upswing in
the late 1990s, thus at times when markets are at moderate levels.
Similarly to my statement in the rent chapter, I argue that the chosen starting
values represent city-specific total yield values at times when they represent
economically reasonable levels. Thus, at these times the total yield value is completely
or almost completely determined by its economic fundamentals and without the
significant influence of other variables. I argue that this is the case here, since at least
for the period captured, the actual total yield level can precisely be forecasted by a
model based on the total yield’s economic fundamentals.130
Thus, the same rule holds for all total yield starting values: They all are
positioned at a point in time where total yields are almost completely determined by
the market forces of demand and supply. Consequently, these points in time represent
good starting values for total yield forecasts which intend to capture the long-run
equilibrium total yield. The short-run phases of total yield volatility and exaggeration
that do not regard economic developments but are induced by, for instance,
speculation or restricted market mechanisms cannot be forecasted by this model.
In this long-run investigation, I used samples starting from 1992 and ending
between 1997 and 2001. When I apply the total sample available from 1992 until 2006
to estimate the multivariate forecasting model, the coefficients are stable and thus in
the same range as in the smaller samples. Hence, starting the forecasts at the chosen
starting point shows a similar pattern for this in-sample forecast compared with the
out-of sample forecast.131 Realizing this, I make the assumption that this pattern - the
determination of the long-run total yield development in the nine German office
markets by only one demand and one supply variable - is also valid for the future. This
conclusion, of course, implies further sub-assumptions such as, for example, that the
free market price mechanism is not prevented from functioning by official authorities
130
Hott & Monnin (2008) who have similar findings in their study give the same interpretation.
131
Estimation and forecasting outputs are not depicted here, but are available upon request.
140
or disturbed by market inefficiencies that last for the long run. Consequently, with
forecasts of the explanatory variables "Office Employees" and the "Office Space
Inventory" up to the desired forecasting horizon, these models, in combination with
the respective starting values, can be applied to even longer-term total yield series outof sample forecasts.
6.4. Chapter Conclusion
In this last subchapter, I analyze whether the research hypotheses presented in chapter
4.1 can be accepted or whether they must be rejected for the total yield examination.
x Research Hypothesis 11: Multivariate regression models are not appropriate for
forecasting total yield series in the German office market.
Rejected: In general, the tested multivariate regression models are able to forecast total
yield series in the German office market. However, one must consider that the
exogenous variables in the multivariate regression models have to be forecasted as
well before being implemented in the model to determine the forecasts of the
endogenous variable. This fact is a considerable source of increased forecasting errors.
x Research Hypothesis 12: There are no economic or real estate variables that
significantly influence the development of the total yield series.
Rejected: The variables studied, “Office Employees”, “Office space inventory”,
“Vacancy; Office space”, “Gross value added; Public & private services”, “Consumer
Price Index, Germany”, “Construction Price Index-new office buildings, Germany”,
“Germany Interbank 12 mth (LDN: BBA) - offered rate”, and “Germany (DEM) IR
Swap 10 Year - middle rate “, and their lag and first difference specifications, show
significant correlations with the total yield series. This is not the case for the variable
“Gross value added; Financial & other services”.
x Research Hypothesis 13: To construct a multivariate regression model which
performs convincingly in forecasting the total yield series, a single demand and
a single supply proxy are not sufficient.
141
Rejected: The first differences of the series “Office Employees” and “Office Space
Inventory” with lag 1 are sufficient to build a multivariate model that generates total
yield forecasts that perform convincingly.
x Research Hypothesis 14: The long-run total yield level is not mainly
determined by its economic fundamentals.
Rejected: According to the graphical analysis, most cities’ actual total yield can
relatively precisely be replicated by the predictions of the multivariate model applying
economic fundamentals. Thus, for these markets, changes in the economic
fundamentals are the prime sources for the long-run development of total yields.
x Research Hypothesis 15: Speculative factors play a role in the long-run
determination of the total yield level.
Rejected: Actual total yield level deviations from the economic fundamentals’
predictions are short-run phenomena due to speculative factors or other market
inefficiencies which do not have long-run influence on the total yield level. In the long
run, only changes in the economic fundamentals have explanatory power for the total
yield level development, as can be seen by the graphs in chapter 6.3.1.
x Research Hypothesis 16: A forecast starting value at a point in time where total
yields are at an economically reasonable level is not crucial to precisely
predicting the total yield level in the longer run.
Rejected: For no city is the respective forecast starting point predicting precise
forecasts for the total horizon situated in a peak. For most of the cities, retracing a total
yield level trough in the mid- or late 1990s and demonstrating a peak around 2000, the
"optimal" starting point is a year when the total yield level is close to the trough or at
the beginning of the upswing in the late 1990s. The starting values chosen represent
city-specific total yield values at times when they represent economically reasonable
levels. Thus, at these times the total yield value is completely or almost completely
determined by its economic fundamentals and without the significant influence of
other variables or speculation. However, the prerequisite of a certain starting value is
less crucial than for the rent series, since the total yield series is measured in relative
terms, and thus forecast errors are not passed on in the future.
142
7.
Conclusion
7.1. Summary of findings
This work is motivated by the research gap evident in the area of forecasting models
for the German office market. Since rent, price, or yield forecasting research is mainly
done by commercially oriented organizations, this work delivers an examination from
a scientific point of view. In this context, the focus is set on an empirical investigation
of several rent and total yield forecasting models for nine major German cities. Their
applicability and performance is analyzed and city- as well as forecasting-horizonspecific patterns are determined and interpreted.
After the literature review, mainly covering Anglo-Saxon research, I derive the
theoretical foundations which are important in executing the empirical part of the
work. Therefore, I theoretically discuss general real estate market characteristics, such
as the coherences of the market with exogenous economic influences, its
inefficiencies, i.e., heterogeneity, high transaction costs, and illiquidity, as well as its
cyclicality. Subsequently, I illustrate the specifics of time series as well as panel data
and I present and evaluate the theoretical fundamentals of common forecasting models
as multivariate regression, ARIMA, ARCH, GARCH, VAR, and VEC. This part is
concluded by giving a brief overview of different forecasting techniques and
performance measures.
The first part of the empirical work contains the rent series investigation. After a
data analysis different city-specific univariate models are constructed and estimated.
Subsequently, these models are used to forecast the rent level. The same is done with
multivariate regression models. The forecasts of these city-specific univariate and
multivariate regression models are then compared and interpreted. Ultimately, models
for long-run forecasts are constructed, estimated, and applied for rent level forecast.
The major findings of this analysis show that ARIMA, GARCH and multivariate
regression models are generally able to forecast rent series in the German office
market. Furthermore, I detected some interesting patterns. GARCH models are able to
outperform single ARIMA models for forecasting horizons of three to five years when
increased volatility appears within the respective city rent series. Moreover, univariate
models outperform multivariate regression models in the short run – one- to three-year
forecasting horizon – in general. On the other hand, parsimoniously constructed
multivariate regression models generally outperform the univariate models in the
longer run. Nevertheless, I detected some cities where this general pattern does not
143
work and where one model dominates the other, independent of time. For instance, the
multivariate regression model dominates for Dusseldorf and the univariate model for
Nuremberg. As illustrated, parsimoniously constructed multivariate regression models
with only one demand and one supply proxy as explanatory variables lead to
considerably better forecasting performances than more complex multivariate
regression models. This fact is also valid for models that are able to forecast up to nine
years for the respective cities. Furthermore, in the long-run regression analysis, I show
that the rent level is mainly determined by its economic fundamentals and that
speculative factors do not play a role, since speculative deviations are eliminated from
the market in the long run. Nevertheless, precise forecasts require certain starting
values, where rents are at an economically reasonable level and thus without
speculative influences. Only if this prerequisite is achieved, are considerable long run
forecasts executable.
The second part of the empirical work contains the total yield series
investigation. The analysis is, to a certain extent, similar to the rent examination. Yet,
due to data restrictions, I was only able to perform the multivariate regression model
scrutiny, with a data analysis, followed by the construction and estimation of the
models as well as the total yield series forecasts. This was also conducted for the long
run.
The major finding of this analysis is the general ability of multivariate regression
models to forecast total yield series in the German office market. Therefore,
parsimoniously constructed models with only one demand and one supply proxy as
explanatory variables lead to considerably better forecasting performances than more
complex models for the one- up to the five-year horizon. The same can be observed for
models with forecasting horizons up to nine years for the respective cities. For the long
run, I additionally demonstrate that the total yield is mainly determined by its
economic fundamentals and that speculative deviations do not play a role. They are
cancelled out of the market in the long run. The rent analysis prerequisite of certain
starting values without speculative influences cannot be neglected but can be
relativized to some extent, since the relative nature of the total yield series does not
pass on forecast errors in the future.
144
7.2. Implications for practice
The results of this work offer certain insights for investors in the German real estate
office market. Along with other factors that have to be considered when composing a
portfolio, such as risk, knowledge of the future return on an investment is crucial when
making investment decisions. Thus, this work focuses on an examination of rent and
total yield forecasts.
A first important finding is the relevance of the forecasting horizon when
deciding on a German office market forecasting model. Short-term investors should
primarily focus on univariate models and their forecasts, whereas investors who are
oriented toward longer investment horizons should prefer to consider the advice from
multivariate models regarding whether to invest in a certain market or not.
Nevertheless, it is definitely useful to take advice from all possible and executable
models132, but focus on the statement from the favorable model when making the final
investment decision. However, one has to keep in mind that this rule could only be
empirically verified for the rent series analysis.
According to this and the assumption for the total yield series that univariate
model forecasts outperform multivariate model forecasts in the short run, it would be
very useful to also have univariate forecasting models for the total yield
examination.133 That is also desirable, since short-term investors will primarily look at
total yield forecasts when deciding on an investment. However, as shown in the
empirical part of this work, no price and thus total yield series long enough for
univariate model estimation could be provided. If longer series are available, in
practice, these should be applied to generate appropriate univariate models to
eventually come to a better basis for decision-making.
Multivariate models proved to deliver precise forecasting values for rents and for
total yield, especially in the long run. This becomes even more impressive if one
considers the parsimonious constitution of the model with only one demand proxy and
one supply proxy. This structure offers an easy application for practitioners with a
need for data for very few variables. Furthermore, these models were estimated with
132
Besides the quantitative models discussed within this work, one could also consider advice from
qualitative models such as, for example, the Delphi method.
133
The assumption can be made since total yield and rent series show similar dependencies and
patterns in the multivariate regression analysis. Thus, I argue that total yield is interpretable similarly
as rent and that univariate model forecasts outperform multivariate model forecasts in the short run.
145
panel data. The efficiency of the models and the precise forecastability for most of the
cities is impressive. However, one might discover exceptions, such as Essen or
Leipzig, where other influences than just the demand and supply proxies seem to be
influential. For these cities, and probably other similar cities which were not under
investigation, separate specific model estimations would be advisable to capture the
other influences and to generate better forecasts for the cities. Nevertheless, under the
current data limitations, with only up to 15 observations per city-variable, that is not
achievable. Another obstacle to consider is that the exogenous variables in the
multivariate regression models also have to be forecasted. Nevertheless, this has to be
done before being implemented in the model to determine the forecasts of the
endogenous variable. This fact is a considerable source of increased forecasting errors.
To cope with the problem, different models could be estimated and their forecasts
compared with those of the original model. Furthermore, scenario analysis could
support statements about future developments, the longer the forecasting horizon
becomes.
Basically, the application of the adopted models is also possible for other office
markets, whether they are in Germany or abroad. Since real estate market
characteristics such as illiquidity, high transaction costs, or cyclicality are the same
worldwide, rent or yield series forecastability is theoretically given. However, this has
to be verified empirically case by case. As should be clear by now, a major
prerequisite is a high quality data base for the respective market which covers
sufficient observations to estimate certain models. But it must be questioned, if this
combination of data quality and quantity is also provided for a variety of smaller
German office markets. For markets abroad good data quality and quantity is provided
for Anglo-Saxon countries, as the broad empirical real estate forecasting literature
suggests. For other countries, scarcely any empirical research exists. Country-specific
data bases should be considered to discover if reasonable model construction is
possible.
7.3. Research Outlook
Some database providers have started to collect more comprehensive data for the
German office market. That, on the one hand, means a greater variety of different
variables. On the other hand, they have started to accumulate quarterly data. That
implies that some years from now these "new" quarterly time series will show a length
146
that enables us to estimate a greater variety of models for the different real estate
market indicators of interest.
Such a development will lead researchers to the point where, firstly, the abovementioned assumption that univariate model forecasts outperform multivariate model
forecasts in the short run can also be tested for total yield series. Furthermore,
multivariate regression models that do not have to rely on panel data can be estimated
and used for forecasting, since more city-specific observations will be available.
Especially for cities such as Essen or Leipzig, it might reveal further influencing
variables that, incorporated into the model, will lead to better performing forecasts.
Additionally, quarterly data will favor the application of VAR and VEC models due to
more available observations and the finer data fragmentation, which leads to clearer
statements regarding causalities. Results of VAR and VEC model forecasts will lead to
new insights, especially in comparison with the other applied models. Moreover, it
would be technically possible to examine the series with respect to seasonalities.
147
Appendix
Appendix Table 1: Unit Root Tests – Rent – Level
Phillips-Perron Test
t-statistics
Test critical values:
(with constant, linear trend)
1% level
5% level
10% level
Null Hypothesis: Cologne has a unit root
Null Hypothesis: Dusseldorf has a unit root
Null Hypothesis: Essen has a unit root
Null Hypothesis: Frankfurt has a unit root
Null Hypothesis: Hamburg has a unit root
Null Hypothesis: Munich has a unit root
Null Hypothesis: Nuremberg has a unit root
Null Hypothesis: Stuttgart has a unit root
p-values
-4.323979
-3.580623
-3.225334
-1.864655
-0.099156
-1.407189
-1.43655
-0.356909
-0.572758
-1.753217
-1.756852
0.6506
0.9928
0.8407
0.8320
0.9852
0.9745
0.7000
0.7038
Appendix Table 2: Unit Root Tests – Rent – 1st Difference
Phillips-Perron Test
t-statistics
Test critical values:
(with constant)
1% level
5% level
10% level
Null Hypothesis: D(Cologne) has a unit root
Null Hypothesis: D(Dusseldorf) has a unit root
Null Hypothesis: D(Essen) has a unit root
Null Hypothesis: D(Frankfurt) has a unit root
Null Hypothesis: D(Hamburg) has a unit root
Null Hypothesis: D(Munich) has a unit root
Null Hypothesis: D(Nuremberg) has a unit root
Null Hypothesis: D(Stuttgart) has a unit root
p-values
-3.65373
-2.95711
-2.617434
-3.067225
-3.03090
-3.883247
-3.300759
-2.513511
-2.458818
-2.622396
-2.769574
Augmented Dickey-Fuller
t-statistics
p-values
-3.661661
-2.960411
-2.61916
0.0391
0.0423
0.0055
0.0227
0.1218
0.1342
0.101
0.0733
-3.270329
-3.210133
-2.264202
-3.935724
-3.684499
-0.638833
-3.086022
-4.415144
0.0255
0.0286
0.1895
0.0054
0.0095
0.8456
0.0402
0.0015
Appendix Table 3: Unit Root Tests – Rent – 2nd Difference
Phillips-Perron Test
t-statistics
Test critical values:
(with constant)
1% level
5% level
10% level
Null Hypothesis: D2(Essen) has a unit root
Null Hypothesis: D2(Munich) has a unit root
p-values
-3.65373
-2.95711
-2.617434
-8.471857
-7.046061
Augmented Dickey-Fuller
t-statistics
p-values
-3.661661
-2.960411
-2.61916
0.0000
0.0000
-3.344596
-6.076033
0.0216
0.0000
148
Appendix Table 4: Unit Root Tests – National Indicators – Level
Phillips-Perron Test
t-statistics
Test critical values:
1% level
5% level
10% level
(with constant, linear trend)
p-values
-4.323979
-3.580623
-3.225334
Null Hypothesis: Consumer Price Index, Germany has a unit root
Null Hypothesis: Construction Price Index, Germany has a unit root
Null Hypothesis: Germany Interbank 12 mth has a unit root
Null Hypothesis: Germany IR Swap 10 Year has a unit root
-1.864655
-0.099156
-1.407189
-1.43655
0.6506
0.9928
0.8407
0.8320
Appendix Table 5: Unit Root Tests – National Indicators – 1st Difference
Phillips-Perron Test
t-statistics
Test critical values:
(with constant)
1% level
5% level
10% level
Augmented Dickey-Fuller
p-values
-3.65373
-2.95711
-2.617434
Null Hypothesis: D(Consumer Price Index, Germany) has a unit root
Null Hypothesis: D(Construction Price Index, Germany) has a unit root
Null Hypothesis: D(Germany Interbank 12 mth) has a unit root
Null Hypothesis: D(Germany IR Swap 10 Year) has a unit root
-3.067225
-3.03090
-3.883247
-3.300759
t-statistics
p-values
-3.661661
-2.960411
-2.61916
0.0391
0.0423
0.0055
0.0227
-3.270329
-3.210133
-2.264202
-3.935724
0.0255
0.0286
0.1895
0.0054
Appendix Table 6: Panel Unit Root Tests – Level 1
Rent
Office employees
Office space inventory
Tests
(with constant, linear trend)
statistics
p-values
statistics
p-values
statistics
p-values
Phillips-Perron - Choi Z-stat:
Null Hypothesis: Series has a unit root
0.74557
0.7720
1.67719
0.9532
-1.62465
0.0521
Hadri - Z-stat:
Null Hypothesis: Series has no unit root
4.06159
0.0000
1.53657
0.0622
5.21038
0.0000
Appendix Table 7: Panel Unit Root Tests – 1st Difference 1
Rent
Office employees
Office space inventory
Tests
(with constant)
statistics
p-values
statistics
p-values
statistics
p-values
Phillips-Perron - Choi Z-stat:
Null Hypothesis: Series has a unit root
-2.49563
0.0063
-1.38405
0.0832
-6.14574
0.0000
Hadri - Z-stat:
Null Hypothesis: Series has no unit root
0.62913
0.2646
-0.57159
0.7162
2.17604
0.0148
149
Appendix Table 8: Panel Unit Root Tests – Level 2
Vacancy
Gross value added, p
Gross value added, f
Tests
(with constant, linear trend)
statistics
p-values
statistics
p-values
statistics
p-values
Phillips-Perron - Choi Z-stat:
Null Hypothesis: Series has a unit root
2.86637
0.9979
1.42650
0.9231
-3.38000
0.0004
Hadri - Z-stat:
Null Hypothesis: Series has no unit root
4.17276
0.0000
3.67985
0.0001
4.21524
0.0000
Appendix Table 9: Panel Unit Root Tests – 1st Difference 2
Vacancy
Gross value added, p
Gross value added, f
Tests
(with constant)
statistics
p-values
statistics
p-values
statistics
p-values
Phillips-Perron - Choi Z-stat:
Null Hypothesis: Series has a unit root
-1.84519
0.0325
-5.73523
0.0000
-8.65753
0.0000
Hadri - Z-stat:
Null Hypothesis: Series has no unit root
-0.16384
0.5651
0.50660
0.3062
-0.26643
0.6050
Appendix Table 10: ARIMA Performance Measures – Cologne
Best-fitting forecasting models
RMSE
MAPE
One-year
ARIMA(4,1,0)
0.159
2.125
Two-year
ARIMA(4,1,0)
0.213
2.447
Three-year
ARIMA(4,1,0)
0.201
2.442
Four-year
ARIMA(4,1,0)
0.597
7.369
Five-year
ARIMA(4,1,0)
1.327
15.714
150
Appendix Table 11: ARIMA Estimation – Cologne
Best-fitting forecasting models
Coefficients
Estimations
p-values
One-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.643
-0.130
0.108
-0.297
0.0177
0.3691
0.3264
0.0000
Two-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.644
-0.134
0.108
-0.295
0.0183
0.3608
0.3303
0.0000
Three-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.651
-0.131
0.103
-0.297
0.0210
0.4449
0.4193
0.0001
Four-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.637
-0.119
0.107
-0.296
0.0252
0.4959
0.3948
0.0001
Five-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.639
-0.114
0.111
-0.297
0.0250
0.5224
0.3818
0.0001
Appendix Table 12: ARIMA Performance Measures – Dusseldorf
Best-fitting forecasting models
RMSE
MAPE
One-year
ARIMA(2,1,0)
0.766
10.073
Two-year
ARIMA(2,1,0)
0.242
2.465
Three-year
ARIMA(2,1,2)
2.017
25.077
Four-year
ARIMA(2,1,0)
3.638
42.209
Five-year
ARIMA(2,1,0)
3.092
32.122
151
Appendix Table 13: ARIMA Estimation – Dusseldorf
Best-fitting forecasting models
Coefficients
Estimations
p-values
One-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.715
-0.139
0.0020
0.4739
Two-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.671
-0.192
0.0260
0.2596
Three-year
ARIMA(2,1,2)
AR(1)
AR(2)
MA(1)
MA(2)
-0.518
-0.111
1.021
0.577
0.1532
0.7176
0.0015
0.0351
Four-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.708
-0.236
0.0035
0.2805
Five-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.708
-0.236
0.0035
0.2805
Appendix Table 14: ARIMA Performance Measures – Essen
Best-fitting forecasting models
RMSE
MAPE
One-year
ARIMA(2,2,0)
0.019
0.364
Two-year
ARIMA(3,2,0)
0.165
3.097
Three-year
ARIMA(2,2,0)
0.074
1.269
Four-year
ARIMA(2,2,0)
0.236
3.914
Five-year
ARIMA(3,2,0)
0.125
1.799
152
Appendix Table 15: ARIMA Estimation – Essen
Best-fitting forecasting models
Coefficients
Estimations
p-values
One-year
ARIMA(2,2,0)
AR(1)
AR(2)
-0.429
-0.587
0.0096
0.0004
Two-year
ARIMA(3,2,0)
AR(1)
AR(2)
AR(3)
-0.273
-0.490
0.245
0.0542
0.0001
0.2144
Three-year
ARIMA(2,2,0)
AR(1)
AR(2)
-0.321
-0.421
0.0354
0.0295
Four-year
ARIMA(2,2,0)
AR(1)
AR(2)
-0.328
-0.418
0.0396
0.0189
Five-year
ARIMA(3,2,0)
AR(1)
AR(2)
AR(3)
-0.255
-0.489
0.342
0.0960
0.0007
0.0796
Appendix Table 16: ARIMA Performance Measures – Frankfurt
Best-fitting forecasting models
RMSE
MAPE
One-year
ARIMA(4,1,0)
0.318
2.544
Two-year
ARIMA(4,1,1)
0.210
1.615
Three-year
ARIMA(4,1,1)
0.797
4.291
Four-year
ARIMA(4,1,1)
2.743
20.975
Five-year
ARIMA(4,1,1)
5.534
39.971
153
Appendix Table 17: ARIMA Estimation – Frankfurt
Best-fitting forecasting models
Coefficients
Estimations
p-values
One-year
ARIMA(4,1,0)
AR(1)
AR(4)
0.558
-0.245
0.0004
0.0220
Two-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
MA(1)
0.026
0.047
-0.084
-0.161
0.997
0.8986
0.7712
0.7441
0.3819
0.0000
Three-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
MA(1)
0.215
-0.079
-0.032
-0.434
0.763
0.2755
0.7140
0.9297
0.0015
0.0000
Four-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
MA(1)
0.013
0.149
-0.023
-0.129
0.913
0.9570
0.6021
0.9514
0.5810
0.0001
Five-year
ARIMA(4,1,0)
AR(1)
AR(4)
MA(1)
0.211
-0.220
0.790
0.3930
0.0496
0.0000
Appendix Table 18: ARIMA Performance Measures – Hamburg
Best-fitting forecasting models
RMSE
MAPE
One-year
ARIMA(2,1,0)
0.305
4.480
Two-year
ARIMA(2,1,0)
0.139
1.826
Three-year
ARIMA(2,1,0)
0.173
2.092
Four-year
ARIMA(2,1,0)
0.594
8.575
Five-year
ARIMA(2,1,0)
1.536
20.977
154
Appendix Table 19: ARIMA Estimation – Hamburg
Best-fitting forecasting models
Coefficients
Estimations
p-values
One-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.902
-0.429
0.0000
0.0137
Two-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.897
-0.403
0.0000
0.0263
Three-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.903
-0.428
0.0000
0.0216
Four-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.849
-0.341
0.0000
0.0354
Five-year
ARIMA(2,1,0)
AR(1)
AR(2)
0.845
-0.297
0.0000
0.0589
Appendix Table 20: ARIMA Performance Measures – Munich
Best-fitting forecasting models
RMSE
MAPE
One-year
ARIMA(2,2,2)
0.000
0.003
Two-year
ARIMA(2,2,2)
0.058
0.761
Three-year
ARIMA(1,2,2)
0.190
2.328
Four-year
ARIMA(1,2,2)
0.807
10.019
Five-year
ARIMA(2,2,2)
7.722
93.673
155
Appendix Table 21: ARIMA Estimation – Munich
Best-fitting forecasting models
Coefficients
Estimations
p-values
One-year
ARIMA(2,2,2)
AR(1)
AR(2)
MA(1)
MA(2)
0.475
-0.088
-0.228
-0.712
0.02
0.7434
0.0759
0.0001
Two-year
ARIMA(2,2,2)
AR(1)
AR(2)
MA(1)
MA(2)
0.490
-0.122
-0.232
-0.690
0.0147
0.6584
0.0874
0.0001
Three-year
ARIMA(1,2,2)
AR(1)
MA(1)
MA(2)
0.358
-0.169
-0.728
0.0399
0.2269
0.0000
Four-year
ARIMA(1,2,2)
AR(1)
MA(1)
MA(2)
0.371
-0.226
-0.800
0.0714
0.1419
0.0002
Five-year
ARIMA(2,2,2)
AR(2)
MA(1)
MA(2)
0.368
-0.113
-0.802
0.0042
0.4075
0.0000
Appendix Table 22: ARIMA Performance Measures – Nuremberg
Best-fitting forecasting models
RMSE
MAPE
One-year
ARIMA(4,1,0)
0.066
1.097
Two-year
ARIMA(4,1,0)
0.068
0.919
Three-year
ARIMA(4,1,1)
0.105
1.708
Four-year
ARIMA(4,1,1)
0.236
3.740
Five-year
ARIMA(4,1,1)
0.090
1.282
156
Appendix Table 23: ARIMA Estimation – Nuremberg
Best-fitting forecasting models
Coefficients
Estimations
p-values
One-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.750
-0.151
-0.104
-0.335
0.0001
0.3774
0.5437
0.0085
Two-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.748
-0.148
-0.107
-0.334
0.0001
0.4075
0.5698
0.0090
Three-year
ARIMA(4,1,1)
AR(2)
AR(4)
MA(1)
0.349
-0.615
0.997
0.0186
0.0024
0.0000
Four-year
ARIMA(4,1,1)
AR(2)
AR(4)
MA(1)
0.398
-0.678
0.965
0.0618
0.0021
0.0000
Five-year
ARIMA(4,1,1)
AR(1)
AR(2)
AR(3)
AR(4)
MA(1)
0.173
0.418
-0.253
-0.522
0.885
0.3631
0.0500
0.2661
0.0241
0.0000
Appendix Table 24: ARIMA Performance Measures – Stuttgart
Best-fitting forecasting models
RMSE
MAPE
One-year
ARIMA(4,1,0)
0.240
3.195
Two-year
ARIMA(4,1,0)
0.177
1.716
Three-year
ARIMA(4,1,0)
0.244
2.927
Four-year
ARIMA(4,1,0)
0.900
11.455
Five-year
ARIMA(4,1,0)
0.954
11.119
157
Appendix Table 25: ARIMA Estimation – Stuttgart
Best-fitting forecasting models
Coefficients
Estimations
p-values
One-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.5040
-0.0449
0.2806
-0.5368
0.034
0.6431
0.0028
0.0000
Two-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.504
-0.045
0.281
-0.537
0.0372
0.6439
0.0029
0.0000
Three-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.525
-0.027
0.306
-0.516
0.0245
0.7545
0.0011
0.0000
Four-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.527
-0.012
0.310
-0.529
0.0230
0.8912
0.0024
0.0000
Five-year
ARIMA(4,1,0)
AR(1)
AR(2)
AR(3)
AR(4)
0.530
-0.011
0.309
-0.530
0.0259
0.8993
0.0027
0.0000
Appendix Table 26: Multivariate Regression Rent Model: Estimation
Best-fitting forecasting models
Coefficients
Estimations
p-values
adj-R-squared
D-W stat
One-year
C
OfEmp
OfSpace
-0.0239
2.1047
-0.4368
0.0013
0.0000
0.0000
0.6052
2.0246
Two-year
C
OfEmp
OfSpace
-0.018
2.064
-0.858
0.0271
0.0000
0.0000
0.6115
1.9909
Three-year
C
OfEmp
OfSpace
-0.019
2.092
-0.861
0.0403
0.0000
0.0000
0.5941
1.9982
Four-year
C
OfEmp
OfSpace
-0.014
1.927
-0.934
0.2041
0.0000
0.0000
0.5611
1.9947
Five-year
C
OfEmp
OfSpace
-0.006
1.728
-0.929
0.4967
0.0000
0.0000
0.6037
2.0889
Note: OfEmp stands for "Office Employees" in logs and first differenced, OfSpace stands for the first lag of "Office Space Inventories" in
logs and first differenced
158
Appendix Graph 1: Cologne Price Series
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Appendix Graph 2: Dusseldorf Price Series
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Dusseldorf
Appendix Graph 3: Essen Price Series
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Appendix Graph 4: Frankfurt Price Series
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Appendix Graph 5: Hamburg Price Series
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Appendix Graph 6: Leipzig Price Series
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Appendix Graph 7: Munich Price Series
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1000
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Munich
Appendix Graph 8: Nuremberg Price Series
1400
1300
1200
1100
1000
900
800
700
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Nuremberg
161
Appendix Graph 9: Stuttgart Price Series
3600
3200
2800
2400
2000
1600
1200
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Stuttgart
Appendix Graph 10: Cologne Yield Comparison
.12
.08
.04
.00
-.04
-.08
-.12
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Total Yield
162
Appendix Graph 11: Dusseldorf Yield Comparison
.2
.1
.0
-.1
-.2
-.3
-.4
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Total Yield
Appendix Graph 12: Essen Yield Comparison
.16
.12
.08
.04
.00
-.04
-.08
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Total Yield
163
Appendix Graph 13: Frankfurt Yield Comparison
.3
.2
.1
.0
-.1
-.2
-.3
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Total Yield
Appendix Graph 14: Hamburg Yield Comparison
.12
.08
.04
.00
-.04
-.08
-.12
-.16
-.20
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Total Yield
164
Appendix Graph 15: Leipzig Yield Comparison
.15
.10
.05
.00
-.05
-.10
-.15
-.20
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Total Yield
Appendix Graph 16: Munich Yield Comparison
.4
.3
.2
.1
.0
-.1
-.2
-.3
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Totla Yield
165
Appendix Graph 17: Nuremberg Yield Comparison
.16
.12
.08
.04
.00
-.04
-.08
-.12
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Total Yield
Appendix Graph 18: Stuttgart Yield Comparison
.2
.1
.0
-.1
-.2
-.3
-.4
92 93 94 95 96 97 98 99 00 01 02 03 04 05 06
Rental Yield
Price Yield
Total Yield
166
Appendix Table 27: Total Yield Panel Unit Root Tests – Level
Total Yield
Tests
(with constant)
statistics
p-values
Phillips-Perron - Choi Z-stat:
Null Hypothesis: Series has a unit root
-2.91596
0.0018
Hadri - Z-stat:
Null Hypothesis: Series has no unit root
0.83516
0.2018
Appendix Table 28: Multivariate Regression Total Yield Model: Estimation
Best-fitting forecasting models Coefficients Estimations
p-values
adj-R-squared
D-W stat
One-year
C
OfEmp
OfSpace
0.0434
2.3633
-0.9454
0.0000
0.0000
0.0000
0.5813
1.8794
Two-year
C
OfEmp
OfSpace
0.038
2.426
-0.711
0.0019
0.0000
0.0218
0.5472
1.8251
Three-year
C
OfEmp
OfSpace
0.030
2.615
-0.581
0.0013
0.0000
0.0385
0.5637
1.8578
Four-year
C
OfEmp
OfSpace
0.031
2.530
-0.569
0.0071
0.0000
0.0533
0.5212
1.8291
Five-year
C
OfEmp
OfSpace
0.038
2.412
-0.643
0.0025
0.0000
0.0427
0.5400
1.8614
Note: OfEmp stands for "Office Employees" in logs and first differenced, OfSpace stands for the first lag of "Office Space
Inventories" in logs and first differenced
167
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Curriculum Vitae
Name: Alexander Bönner
Born: July 26, 1978 in Wuppertal, Germany
Education
10/2006 – 10/2008:
Doctoral studies in Banking & Corporate Finance
University of St. Gallen, Switzerland
10/2004 – 10/2006:
Master in Banking and Finance
University of St. Gallen, Switzerland
01/2005 – 04/2005:
Exchange term
R. Ivey School of Business, London, Canada
10/2001 – 10/2004:
Bachelor in Economics
University of St. Gallen, Switzerland
Work Experience
Since 09/2007:
Research Associate with Prof. Dr. Dr. h.c. Klaus Spremann
Swiss Institute of Banking and Finance, University of St. Gallen,
Switzerland
07/2006 – 09/2006:
Internship: Strategic financing of mid-cap businesses (Advisory)
PricewaterhouseCoopers, Düsseldorf, Germany
05/2005 – 06/2005:
Internship: Accounting department (industry, mid-cap)
MedTech Wristbands, London, Canada
08/1999 – 07/2001:
Bank traineeship
Deutsche Bank AG, Wuppertal, Germany